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History of the Calendar

in Different Countries Through the Ages

M.N. Saha

and
N.C. Lahiri

COUNCIL OF SCIENTIFIC & INDUSTRIAL RESEARCH
Rafi Marg, New Delhi- 1 10001
1992

Part C of Report of Calendar Reform Committee,
Government of India

First published: 1955
Reprinted: 1992

Printed by Publications & Information Directorate
Dr K.S. Krishnan Marg, New Delhi -110012

FOREWORD

The Council of Scientific & Industrial Research (CSIR) of the Government of India appointed a Calendar
Reform Committee under the chairmanship of Prof. Meghnad Saha in November 1952. The Committee was
entrusted with the task of 'examining all the existing calendars which are being followed in the country at
present and after a scientific study of the subject, submit proposals for an accurate and uniform calendar for
the whole of India'. The following were the members of the Committee:

Prof. M.N. Saha, D.Sc, RR.S., M.P. (Chairman)

Prof. A.C. Banerji, Vice-Chancellor, Allahabad University

Dr. K.L. Daftari, Nagpur

Shri J.S. Karandikar, Ex-Editor, The Kesari, Poona
Dr. Gorakh Prasad, D.Sc., Allahabad University
Prof. R.V. Vaidya, Madhav College, Ujjain
Shri N.C. Lahiri, Calcutta (Secretary)

Dr. Gorakh Prasad and Shri N.C. Lahiri came in place of Prof. S.N. Bose and Dr. Akbar Ali who were
originally appointed but were unable to serve.

The Committee's Report was submitted to CSIR in 1955 and the Government, in accepting the recom-
mendations of the Committee, decided that 'a unified National Calendar' (the Saka Calendar) be adopted for
use with effect from 21 March 1956 A.D., i.e., 1 Chaitra 1878 Saka. The Report of the Calendar Reform
Committee was published by CSIR in 1955. Part C of the Report consisting of a review of 'History of the
calendar in different countries through the ages' by Prof. M.N. Saha and Shri N.C. Lahiri was also published
separately. This useful publication has been out of print for some time and scientists in general, and
astronomers in particular, have been conscious of the non-availability of this valuable review. Therefore, the
CSIR has decided to reprint it. No changes have been made from the original except that 'Corrigenda and
Addenda' have been incorporated into the text, and consequently the bibliography and the index (which
pertain to the whole report) have been repaginated. The title page of the Report, Jawaharlal Nehru's message,
and Saha & Lahiri 's preface have also been included in the present volume.

I hope that this reprinted volume will be found useful and informative by calendaric astronomers, science
historians and scientists in general.

S.K. Joshi

New Delhi Director-General

15 August 1992. Council of Scientific & Industrial Research

and Secretary,

Department of Scientific & Industrial Research

FACSIMILE OF ORIGINAL COVER

REPORT

OF THE

CALENDAR REFORM COMMITTEE

GOVERNMENT OF INDIA

Council of Scientific and Industrial Research,
Old Mill Road,
New Delhi.
1955

MESSAGE

I am glad that the Calendar Reform Committee
has started its labours. The Government of India
has entrusted to it the work of examining the
different calendars followed in this country and to
submit proposals to the Government for an accurate
and uniform calendar based on a scientific study
for the t^hole of India. I am told that we have at
present thirty different calendars, differing from
each other in various ways, including the methods
of time reckoning. These calendars are the natural
result of our past political and cultural history
and partly represent past political* divisions in
the country. Now that we have attained independence,
it is obviously desirable that there should be a
certain uniformity in the calendar for our civic,
social and other purposes and that this should be
based on a scisntific approach to this problem.

It is true that for governmental and many
other public purposes we follow the Gregorian
calendar, which is used in the greater part of the
world. The mere fact that it is largely used, makes
it important. It has many virtues, but even this
has certain defects which make it unsatisfactory
for universal use.

It is always difficult to change a calendar
to which people are used, because it affects social
practices. But the attempt has to be made even though
it may not be as complete as desired. In any event,
the present confusion in our own calendars in India
ought to be removed.

I hope that our Scientists will give a lead
in this matter.

New Delhi,
February 18, 1953.

MEMBERS OF THE CALENDAR REFORM COMMITTEE

CHAIRMAN

Prof.

M. N. Saha, D. Sc., F. R. S., M, P.,

Director, Institute of Nuclear Physics,
92, Upper Circular Road, Calcutta-9.

MEMBERS

Prof,

A. C. Banerji, M. A M M. Sc., F. N. I.,

Vice-Chancellor, Allahabad University,
Allahabad.

Dr. K. L. Daftari, B. A., B. L M D. Litt.,

Mahal, Nagpur.

Shri J. S. Karandikar, B. A., LL. B.,

Ex -Editor, The Kesari,
568 Narayan Peth,
Poona-2.

Dr. Gorakh Prasad, D. Sc.,

Reader in Mathematics, Allahabad University,
Beli Avenue, Allahabad,

Prof. R. V. Vaidya, M. A., B. T M

Senior Lecturer in Mathematics, Madhav College, Ujjain,
78, Ganesh Bhuvan, Freegunj, Ujjain.

Shri N. C. Lahiri, M. A.,

55A, Raja Dinendra Street, Calcutta-6.

Shri N. C. Lahiri acted as the Secretary of the Committee.

TRANSLITERATION

The scheme of transliteration of Sanskrit alphabets into Roman script adopted in this publication is the
same as generally followed. The corresponding scripts are given below : —

VOWELS

CONSONANTS

P
b

ch
3

th
d

dh
n

th
d

dh
n

N* B. Diacritical marks have not generally been used in names of persons belonging to recent times
as well as in well-known geographical names.

PREFACE

The Calendar Reform Committee was appointed
in November, 1952, by the Council of Scientific and
Industrial Research (of the Government of India) with
the following terms of reference :

"To examine all the existing calendars which are fceing
followed in the country at present and after a scientific
study of the subject, submit proposals for an accurate and
uniform calendar for the whole of India".

In accordance with its terms of reference, the
Committee (for personnel, see p. 4) has scientifically
examined all the calendars prevalent in India (vide
Part C, Chap. V), viz*, —

Gregorian Calendar*.. which is used for civil and
administrative purposes (vide
p. 170) all over the world.

Islamic Calendar used for fixing up the dates

of Islamic festivals (vide
p. 179).

Indian Calendars

or Pancangas used for fixing up dates and

moments of Hindu, Bauddha
and Jaina festivals in different
States of India* and in many
cases for civil purposes also.
They are about 30 in number.
(vide Chap. V, p. 258).
It has been pointed out (p. 171) that the Gregorian
calendar, which is used all over the world for civil
and administrative purposes, is a very unscientific and
inconvenient one. The World Calendar (p* 173),
proposed by the World Calendar Association of New
York, has been examined and found suitable for
modern life. The proposal for its adoption by all the
countries of the world for civil and administrative
purposes was sponsored by the Indian Government
before the U. N. O. and debated before the ECOSOC
(Economic and Social Council) at Geneva in June,
1954 (p. 173) and its recommendations have been
transmitted to the Governments of the World for
their opinion. It is hoped that the World Calendar
will be ultimately adopted. It will lead to a great
simplification of modern life.

The introduction of the World Calendar in place
of the Gregorian is a matter for the whole world,
which has now to look for decision by the U, N. O.

The Islamic (Hejira) calendar has been discussed
on p, 179, along with some proposals for reform

suggested by Dr. Hashim Amir Ali of the Osmania
University, and Janab Mohammed Ajmal Khan of the
Ministry of Education. It is for the Islamic world to
give its verdict on these suggestions. If these sugges-
tions are accepted, the Islamic calendar would fall in
line with other luni-solar calendars.

As these two important systems of calendars had
to be left out, the Committee's labours were confined
to an examination of the different systems of calendars
used by Hindus, Bauddhas and Jainas in the different
states of India, chiefly for the fixing up of the dates
and moments of their religious festivals, and for
certain civil purposes as well.

For the purpose of examining all the existing
calendars of India, as per terms of reference, an appeal
was issued to the Paricanga (Almanac) makers for
furnishing the Committee with three copies of their
Pancangas. In reply to our request 60 Pancangas
(Almanacs) were received from different parts of the
country and were examined (p. 21). To facilitate
examination of the calendars, a questionnaire was
issued to which 51 replies were received (pp. 23-31).
In addition to the above, 48 persons offered their
suggestions (pp. 32-38) for reform of the Indian
calendar. These views were very divergent in
character. Some quoted ancient scriptures to prove
that the earth is flat, with a golden mountain in the
centre round which move the sun and the planets,
others tried to refute the precession of equinoxes.
All opinions were taken into consideration in arriving
at the decisions of the Committee.

Principles followed in fixing up the Calendar : — The
calendar has got two distinct uses— civil and religious.
The Indian Calendars are used not only for fixing up
the dates and moments of religious observances but
also for the purpose of dating of documents and for
certain civil purposes not only by the rural, but also
by a large section of the urban population. There is
great divergence in practice in different parts of the
country in this respect. Therefore a unified solar
calendar has been proposed for all-India use for civil
purposes. This has been based on the correct length
of the year (viz. the tropical year) and the popular
month-names, vix. % Caitra, Vaisakha, etc. have been
retained (see p. 6).

Calendars are based partly on SCIENCE which
nobody is permitted to violate and partly on
CONVENTIONS which are man-made and vary from

PREFACE

place to place. The Indian calendars put up by
almanac-makers commit the violation of the following
principles of science : —

They take the length of the year to be 365.258756
days (p. 240, Part C of Report) as given by the Surya~
Biddhdnta about 500 A. D. ; while the correct length
of the tropical year, which alone can be used according
to the Surya-SiddJ&nta and modern astronomy for
calendarical use, is 365.242196 days. The difference
of .01656 days is partly due to errors of observation,
not infrequent in those days, and to their failure to
recognize the precession of equinoxes. As the Surya-
Siddhanta value of the year-length is still used in
almanac-making, the year-beginning is advancing by
.01656 days per year, so that in the course of nearly
1400 years, the year-beginning has advanced by 23.2
days, with the result that the- -Indian solar year,
instead of starting on the day following the vernal
equinox, i.e., on March 22, as prescribed in the Surya-
Siddhanta (see Chap. V, p. 239), starts on April 13 or
14. The situation is the same as happened in Europe
due to the acceptance of 365.25 days as the length of
the year at the time of Julius Caesar ; the Christmas
originally linked to the winter solstice preceded it
by 10 days by 1582 A.D., when the error was
rectified by the promulgation of a bull by Pope
Gregory XIII. By this, Friday, October 5 was
proclaimed as Friday, October 15, and new leap-year
rules were introduced.

Unlike Europe, where the Pope in the medieval
times possessed an authority which every one in
Catholic Europe respected, India had a multiplicity
of eras and year^beginnings due to her history during
the years 500-1200 A. D. But for calendaric calcula-
tions, our astronomers all over India have been using
only the Saka era since Aryabhata (500 A.D.) certainly
and probably from much earlier times, and in local
almanacs other eras are simply imposed on it. The
Calendar Committee has therefore recommended : —

That for all official purposes, the Central as well
as State Governments should use the Saka era along
with the civil calendar proposed by the Committee
(p.6). -It is suggested that the change-over may take
place from the Saka year 1878, Caitra 1 (1956, March
21}. If this is accepted, the last month of the year, viz. %
1877 Saka, the solar Phalguna, which has a normal
length of 30 days, will have an extra number of 6 or
7 days. -

The pre-eminence of the Saka era is due, as
historical evidences cited on pp. 228-238 and 255-257
show, that it was the earliest era introduced in India,
by Saka ruling powers, and have been used exclusively
by the Sakadvlpi Brahmins (forming the astrologer
■caste) for calendar-making on the basis of Siddhantic

(scientific) astronomy evolved by Indian astronomers
on the basis of old Indian calendaric conceptions,
which were put on scientific basis by blending with
them astronomical conceptions prevalent in the West,
from the third century B.C.

The era is also used exclusively for horoscope
making, a practice introduced into India since the
first century A.D. by the Sakadvlpi Brahmanas.

The Calendar Committee has devised a solar
calendar with fixed lengths of months for all-India use,
in which it has been proposed to give, up the
calculations of the Surya-Siddhanta in which the
solar months vary from 29 to 32 days.

Religious Calendar — The Committee's task resolved
itself into a critical examination of the different
Indian local calendars, about 30 in number, which
use different methods of calculation. This produces
great confusion.

As already stated the Surya-Siddhanta year being
longer than the tropical year by about 24 mins., the
Hindu calendar months have gone out of the seasons
to which they conformed when the Siddhantic rules
were framed ; as a result, the religious festivals are
being observed not in the seasons for which they were
intended but in wron* seasons. The Committee felt
that the error should be corrected once for all and
the months brought back to their original seasons.
But with a view to avoiding any violent break in the
present day practices, the desired shifting has not
been effected, but any further increase of the error has
been stopped by adopting the tropical year for our
religious calendar also (sec p. 7).

Before the rise of Siddhanta Jyotisa ( 400 A.D. ),
India used only the lunar calendar calculated according
to the Vcdahga Jyotifa rules and most religious festi-
vals ( e.g. the Janm3ftami, the birthday of Sri Krsna )
used to be fixed up by the lunar calendar which used
only t i tli i and naksatra. The Calendar Committee
could not find out any way of breaking off with the
lunar affiliation short of a religious revolution and
has, therefore, decided to keep them. For this
purpose, the lunar year is to be pegged on to the solar
year by a number of conventions. The Committee has
adhered to the ancient conventions as far as possible.
But the erroneous calculations of tithis and naksatras
have been replaced by modern calculations given in
the nautical almanacs and modern ephemcrides, and
the religious holidays have been fixed for a central
station of India ( tide page 40 ).

The present practice is to calculate the tithi for
each locality and the result is that the same tithi
may not occur on the same day at all places. The
Calendar Committee has found that the continuance

PREFACE

of different lunar calendars for different places is a
relic of medieval practice when communication was
difficult, the printing press did not exist and
astrologers of each locality used to calculate the
calendar for that locality based on Siddhantic rules
and used to proclaim it on the first day of the year
to their clients. In these days of improved communi-
cation, free press, and radio, there is not the slightest
justification for continuance of this practice and the
Committee has fixed up the holidays for the central
station (82° 30' E, 23° 11' N, see Report p. 40);
and recommended that these holidays may be used for
the whole of India. The dates of festivals of the
Hindus, Jainas and Bauddhas have been determined on
the above basis. This will put an end to the calendar
confusion.

The confusion is symbolic of India's history.
While all Christendom comprising people of Europe,
Asia and America, follows the Gregorian calendar,
and the whole of the Islamic world follows the Hejira
calendar for civil and religious purposes, India uses 30
different systems for fixing up the same holidays in
different parts of the country and frequently, two
rival schools of pancanga-makers in the same city fix
up different dates for the same festival. This is a
state of affairs which Independent India cannot
tolerate. A revised national calendar, as proposed
by us, should usher a new element of unity in
India.

The Committee has therefore gone deeply into the
history of calendar making in all countries from the
earliest times particularly into the history of calendar-
making in India (vide Chap. V) and has arrived at their
conclusions. Its recommendations are entirely in
agreement with the precepts laid down by the Siddhan-
tic astronomers, as given in the Stirya-Siddhanta and
other standard treatises (see p. 238 et seq.).

The Committee has also compiled a list of all reli-
gious festivals observed in diffirent parts of India and
listed them under the headings (i) Lunar, and (ii) Solar,
with their criteria for fixing the dates of their obser-
vances (pp. 102-106).

Where does the Government come in : Though India
is a secular state, the Central Government and the
State Governments have to declare a number of holi-
days in advance, a list of which. will be found on pages
117-154 for the Central Government as well as for the
States. These holidays are of four different kinds,
viz. : —

(i) Holidays given according to the Gregorian
calendar, e.fi,, Mahaima Gandhi's birthday,
which falls on Oct. 2. These present no
problem to any government.

(ii) But there are other holidays, which are given
according to the position of the Sun (vide
pp. 117-118).

(iii) Others which are given according to thb luni-
solar calendar (pp. 119-124).

(iv) Holidays for Moslems and Christians (pp. 125
and 126).

* It is a task for the Central as well as State Govern-
ments to calculate in advance dates for the holidays it
gives. This is done on the advice of Pancanga-makers
attached to each Government. In addition, numerous
indigenous pancangas arc prepared on the Siddhantic
system of calculations, the elements of which arc now
found to be completely erroneous. There is a wide
movement in the country first sponsored by the
great savant, patriot and political leader, the late
Lokamanya B. G. Tilak, for making the pancaiiga
calculations x>n the basis of the correct and up-to
date astronomical elements. As a result, there are
almost in every State different schools of pancariga
calculations, differing in the durations of tithis,
naksatras, etc., and consequently in the dates of
religious festivals. The problem before the Govern-
ment is : which one of the divergent systems is to be
adopted. The Committee has suggested a system of
calculations for the religious calendar also, based on
most up-to-date elements of the motion of the sun and
the moon. Calendars for five years from 1954-55 to
1958-59 have been prepared on this basis showing
therein inter alia the dates of important festivals of
different States (vide pp. 41-100). The lists of holidays
for the Government of India and of each separate
State for the five years have also been prepared from
this calendar for the use of the Governments. The
Committee hopes that the Government of India as well
as the State Governments would adopt these lists in
declaring their holidays in future. The Ephcmerides
Committee which has been formed by the Government
pi India, consisting of 'astronomers versed in the
principles of calendar-making would act as advisers to
the Central as well as State Governments. It may be
assisted by an advisory committee to help it in its
deliberations.

The responsibility of preparation of the five-yearly
calendar and the list of holidays on the basis of
recommendations adopted by the Committee has been
shared by Sri N. C. Lahiri and Sri R. V. Vaidya,
aided by some assistants and several pandits of notjc,
amongst whom the following may be mentioned :
Sri A. K. Lahiri, Sri N. R. Choudhury, Pandit
Narendranath Jyotiratna, and Joytish Siddhanta
Kesari Venkata.Subba Sastry of Madras.

We have received great help from C. G. Rajan,
B.A., Sowcarpet, Madras. He has kindly furnished

xii

us with valuable suggestions regarding 'Rules for
fixing the dates of festivals for South India*.

We are indebted to the Astronomer Royal of Great
Britain, Sir Harold Spencer Jones, and to Mr. Sadler,
head of the Ephemcrides divison of the Royal
Observatory of U. K. for having very kindly supplied
us with certain advance data relating to the sun and
the moon which have facilitated our calculations. We
have to thank the great oriental scholar, Otto Ncuge-
bauer for having helped us in clearing many obscure
points in ancient calcndaric astronomy. We wish to
express our thanks to Prof. P. C. Scngupta for helping
us in clearing many points of ancient and medieval
Indian astronomy.

We have reproduced figures from certain books
and our acknowledgement is due to the publishers. It
was however not possible to obtain previous permission
from them, but the sources have been mentioned at
the relevant places.

It is a great pleasure and privilege to express our
gratitude to our colleagues of the Calendar Committee
for their active co-operation in the deliberations of the
Committee, and ungrudging help whenever it was
sought for.

M. N. Saha
Calcutta, Chairman
The 10th Nov., 1955. N. C. Lahiri

Secretary

REPORT

OF THE

CALENDAR REFORM COMMITTEE

PART C

History of the Calendar in different
Countries through the Ages

Prof. M. N. SAHA, d. sc., f. r. s.

Professor Emeritus, University of Calcutta,
Chairman, Calendar Reform Committee,

AND

Sri N. C. LAHIRI, m. a.

Secretary, Calendar Reform Committee.

CONTENTS

PART C

History of the Calendar in different countries through the ages

CHAPTER

PAGE

CHAPTER

PAGE

I — General Principles of Calendar Making

157-163

4.6

The Zodiac and the Signs

1.1

Introduction

... 157

4.7

Chaldean contributions to astronomy:

1.2

The natural periods of time

Rise of planetary and horoscopic

astrology

1.3

The problems of the Calendar

... 158

4.8

Greek contributions to astronomy

1.4

Subdivisions of the day

... 159

4.9

Discovery of the precession of the

1.5

Ahargana or heap of days: Julian days

... 161

equinoxes

11— The Solar Calendar

164-173

Appendix:

2.1

Time reckonings in ancient Egypt

... 164

4-A-

—Newton's explanation of the precession

2.2

Solar calendars of other ancient nations

... 165

of the equinoxes

2.3

The Iranian Calendar

... 166

4-B — Stars of the lunar mansions

2.4

The French Revolution Calendar

... 167

2.5

The Roman Calendar

... 168

V — Indian Calendar

2.6

The Gregorian Calendar

... 170

5.1

The periods in Indian history

2.7

The World Calendar

... 171

5.2

Calendar in the Rg-Vedic age

5.3

Calendaric references in the

III — The Luni-Solar and Lunar Calendars

174-180

Yaj ur- Vedi c 1 i terature

3.1

Principles of Luni -solar calendars

174

5.4

The Vedanga Jyotisa Calendar

3.2

Moon's synodic period or lunation:

5.5

Critical review of the inscriptional

Empirical relation between the year and

records about calendar

the month

... 175

5.6

Solar Calendar in the Siddhanta Jyotisa

3.3

The Luni-solar calendars of the

period

Babylonians the Macedonians, the

5.7

Lunar Calendar in the Siddhanta Jyotisa

Romans and the Jews

... 176

period

3.4

The introduction of the era

... 177

5.8

Indian Eras

3.5

The Jewish Calendar

... 179

3.6

The Islamic Calendar •

... 179

Appendix:

5-A

— The Seasons

IV — Calendaric Astronomy

181-211

5-B

— The Zero-point of the Hindu Zodiac

4.1

The Moon's movement in the sky

... 181

5-C

— Gnomon measurements in the Aitareya

4.2

Long period observations of the moon:

Brahmana

The Chaldean Saros

... 184

5-D

— Precession of the Equinoxes amongst

4.3

The Gnomon

... 188

Indian Astronomers

4.4

Night observations: the celestial pole

5-E-

— The Jovian years

and the equator

... 190

4.5

The apparent path of the sun in the sky:

Bibliography

The Ecliptic

... 191

Index

192

194
201

204

... 207
... 210

212-270
212
214

218
221

226

234

245
251

. 259
262

.. 266

267
.. 270

. 271
. 273

CHRONQ1 OGjCAL TABLE

-3500

-3000

-2500

INDUS -
VALLEY
CIVILISATION

■2000

-1500

-WOO

-500

500

WOO

1500

2000

India

VED1C
PERIOD

IRAN

Mesopotamia

ELAM

VEDANGA
CALENDAR

\BUDDHA

A C

SUMER

AKKAD

Urfll

SYR! A

\HAMMURABi\
KA5SSTES

PYRAMIDS
OLD KINGDOM

HYK

MIDDLE KBiSWM

SOS

ASSYRIA

) NABONASSAfi\

CHALDEAN

H E M E N i D

MAURYA
BACTRIAN
GREEK

SAKA

KUSHAN

GUPTA

AftYABHAm

MEDIEVAL
DYNASTIES

\BNASKARA 1

ISLAMIC
PERIOD

\AKBAR\

BRITISH
PERIOD

— f 1"

E M P / RE

SELEUCID EMPIRE
PARTHIAN EMPIRE

S ASS AN ID EMPIRE

\CHRIST)r

/SLA MIC C A L / PHA

EGYPT

SOTHfC
CYCLE

Asia minor

Greece

ITALY *
EUROPE

NEW KINGDOM

PTOLEMA/C
DYNASTY

HITTITES

CRETE

HOMERIC
GREEKS

GREEK
ALPHABET
OLYMPIC
ERA

GREEK
CITY STATES

\ALEXAliDER\

FOUNDATION
OF ROME

ITALIAN
CITY STATES

\HIPPARCHUS

EMPIRE
\PT OLEMAlOS\

OF H O M

\f£

BYZA NTiNE_ E_MPJPE,

\rAESAR\

END OF ROMAN

EMPIRE

DARK
AGE

RENAISSANCE

\COPERNICUS

\GREGORY2M

INDUSTRIAL
REVOLUTION

'3500

•3000

-2500

-2000

-1500

-1000

-500

500

1000

1500

2000

THE ZODIAC THROUGH THE AGES

MAGNITUDES

First •

SECOND •

Third •
Fourth .

F\FTH

positions or the: first point or

ARIES (T) IN Dl TFE.RENT TIMES.

V = VeJic Times ahoul 2300 B.C.
/f = Hipparchoj UO B.C.

PiU Ptolemy 150 A.D.

Sj - Surya SicJdhan/a 2.85 A.D.

S 2 « , 500 A.D.

Sj =r 510 AD.

M = Modern 1950 A.D.

CHAPTER I

General Principles

1.1 INTRODUCTION

The Flux of Time, of which we are all conscious, is
apparently without beginning or end, but it is cut up
periodically by several natural phenomena, vix. :

(1) by the ever-recurring alternation of daylight
and night,

(2) by the recurrence of the moon's phases,

(3) by the recurrence of seasons.

If is these recurring phenomena which are used to
measure time.

These phenomena have the greatest importance for
man, for they determine all human and animal life.
Even prehistoric men could not help noticing these
time-periods, and their effect on life.

When human communities started organized social
life in the valleys of the Indus and the Ganges (India),
the Nile (Egypt), the Tigris and the Euphrates
(Mesopotamia) and the Hoang Ho (China), several
millenia before Christ (vide Chronological Table), these
phenomena acquired new importance. For these early
societies were founded on agriculture ; and agricultural
practices depend on seasonal weather conditions.
With these practices, therefore, grew national and
religious festivals, necessary for the growth of social
life, and of civilization. People wanted to know in
advance when to expect the new moon or the full moon,
when most of the ancient festivals were celebrated ;
when to expect the onset of the winter or the
monsoon ; when to prepare the ground for sowing ;
the proper time for sowing and for harvesting.
Calendars are nothing but predictions of these events,
and were early framed on the basis of past experiences.

1.2 THE NATURAL PERIODS OF TIME

The three events mentioned in (1), (2) and (3) above
define the natural divisions of time. They are :

The Day : defined by the alternation of daylight
and night.

The Month : the complete cycle of moon's changes
of phase, from end of new-moon to next end of new-
moon (amdnta months), or end of full-moon to end
of next full-moon {purnimUnta months).

The Year : and its smaller subdivisions, viz., the
seasons.

: Calendar Making

The Day* :

The day, being the smallest unit, has been taken as
the fundamental unit of time and the lengths of months,
the year and the seasons are expressed in terms of the
day as the unit.

But the day is to be defined. Many early nations
defined the day as the time-period between sunrise
to sunrise (savana day in India) or sunset to sunset
(Babylonians and Jews). But the length of the day,
so defined, when measured with even the rough
chronometers of early days, was found to be variable.
This is due to the fact that except at the equator, the
sun does not rise or set at the same time in different
seasons of the year. So gradually the practice arose
of defining the day as the period from midnight to
midnight, i. e., when the sun is at the nadir to its next
passage through the nadir. Even then the length of
the day is found to be variable when measured by an
accurate chronometer. The reasons are set forth in all
astronomical text books. Then came the idea of the
mean solar day, and it is now taken as the funda-
mental unit of time. The mean solar day is -the
average interval between the two successive passages
of the sun over the meridian of a place derived from a
very large number of observations of such meridian
passages. The time between two passages is measured
by an accurate chronometer.

In addition to the solar day, the astronomers define
also a sidereal day, which is the time period between
two successive transits of a fixed star. It measures
the time of rotation of the earth round its axis.t

The solar day is larger than the sidereal day,
because by the time the earth completes a rotation
about its axis, the sun slips nearly a degree to the east,
due to the motion of the earth in its orbit, and it
takes a little more time for the sun to come to the

* Day here means 'Day and Night'. In ancient times, the
duration of day-light from sunrise to sunset, and of : the night from
sunset to sunrise, were measured separately with the aid of water-
clocks. It was comparatively late that the length of the Day, meaning
day-light and night, was measured. It was distinguished by the term
ahoratra in Sanskrit, ahna meaning daylight time, and rain meaning
night time. In Greece, this was known as Nychthemeron.

+ Actually speaking, the sidereal day is defined in astronomy as
the period between two successive meridian passages of the First
point of Aries. As this point has a slow westward motion among
the fixed stars, the duration of the so called sidereal day is very
slightly less than the actual sidereal day or the period of rotation of
the earth.

158

REPOKT OF THE CALENDAR REFORM COMMITTEE

meridian of the place. We have the relation :
365J mean solar days«366J sidereal days.
Rotation of the earth =23 b 56™ 4M00 mean solar time.
Sidereal day = 23 56 4.091 „ » »

Mean solar day =24 3 56.555 sidereal time

The actual sidereal day, which measures the period
of rotation of the earth is generally taken to be cons-
tant. The variable part of the solar day comes from
two factors :

(1) Obliquity of the sun's path to the equator,
and

(2) Unequal motion of the sun in different parts
of the year.

(See H. Spencer Jones, General Astronomy p. 45).
It has however been recently found that even the
period of rotation of the earth is not constant but
fluctuates both regularly and irregularly by amounts
of the order of 10- • seconds. &

The Month :

The month is essentially a lunar phenomenon, and
is the time-period from completion of new moon
{conjunction of moon with the sun) to the next new
moon. But the length of the month so defined varies
from 29.246 to 29.817 days, owing to the eccentricity
of the moon's orbit and other causes. The month or
lunation used in astronomy is the mean synodic
period, which is the number of days comprised within
a large number of lunations divided by the number of
lunations. Its value is given by

1 lunation = 29. d 5305882— O. d 0000002 T
where T = no. of centuries after 1900 A.D.

The present duration of a lunation *= 29*5305881
days or 29 d 12 h 44 m 2. s 8. There are other kinds of
months derived from the moon and the sun which
will be discussed later.

The Year and the Seasons :

The year is the period taken by the seasonal
characteristics to recur. The early people had but a
vague notion, of the length of the year in terms of
the day. In the earliest mythology of most nations,
the year was taken to have comprised 360 days, consis-
ting of 12 months each of 30 days. They apparently
thought that the moon's phases recur at intervals of
30 days.

But experience soon showed that these measures
of the month and the year were wrong, but they have
left their stamp on history. The sexagesimal measure
used in astronomy and trigonometry, as well as fanci-
ful cycles of life of the Universe, invented by ancient
nations, appear to have been inspired by these
numbers.

It appears that the Egyptians found very early
(as related in the next section) from the recurrence
of the Nile floods that the year had a length of 365
days. Later they found the true length to be nearer
365.25 days.

The ancient Babylonians, or Chaldeans as they
were called from about 600 B.C., appear to have been
the earliest people who tried to obtain correct
measures of the time-periods ; the month, the year,
and the seasons in terms of the day, and its subdivi-
sions. Their determinations were transmitted to
the Greeks who refined both the notions and measure-
ments very greatly. This story will be told in
Chapter II.

At present it is known that the length df the
seasonal year (tropical year) is given by :—

Tropical year = 365-24219879— '0*614 (t— 1900) days,
where t= Gregorian year.

The present duration of a tropical year is
365*2421955 days or 365 d 5 h 48 m 45-7.

The Sidereal Year :

In some countries, the ancients took the year to
be the period when the sun returned to the same
point in its path (the ecliptic). This is the time of
revolution of the earth in its orbit round the sun.
The tropical year, or the year of seasons, is the time
of passage of the sun from one vernal equinox
to the next vernal equinox. The two years would
have been the same, if the vernal equinoctial point
(hereafter called the vernal point) were fixed. But
as narrated in Chapter IV, it recedes to the west at
the rate of 50" per year. The tropical year is there-
fore less than the sidereal year by the time taken by
the sun to traverse 50% i.e., by .014167 days or
20 m 24 s .

For calendarical purpose, it is unmeaning to use
the sidereal year (365 d . 256362), as then the dates
would not correspond to seasons. The use of the
tropical year is enjoined by the Hindu astronomical
treatises like the Surya Siddhanta and the PaMca
Siddhantika. But these passages have been misunder-
stood, and Indian calendar makers have been using
the sidereal year with a somewhat wrong length
since the fifth century A.D.

1.3 THE PROBLEMS OF THE CALENDAR

Whatever may be the correct lengths of the astro-
nomical month and the year, for application to human
life, the following points have to be observed in
framing a civil calendar.

(a) The civil year and the month must have an
integral number of days.

GEHERAL PEINCIPLES OF CALENDAR MAKING

159

(b) The starting day of the year, and of the month
should be suitably defined. The dates must correspond
strictly to seasons.

(d) The civil day, as distinguished from the
astronomical day, should be defined for use in the
calendar.

(e) If the lunar months have to be kept, there
should be convenient devices for luni-solar adjustment.

A correct and satisfactory solution of these pro-
blems has not yet been obtained, though in the form
of hundreds of calendars which have been used by
different people of the world during historical times,
we have so many attempted solutions. The early
calendars were based on insufficient knowledge of the
duration of the natural time cycles— day, month and
year — an ^ l e( l to gross deviations from actual facts,
which had to be rectified from time to time by the
intervention of dictators like Julius Caesar, Pope
Gregory XIII, or a founder of religion like Mohammed,
or by great monarchs like Melik Shah the Seljuk, or
Akber, the great Indian emperor.

Owing to the historical order of development,
calendars have been used for the double purpose :

(i) of the adjustment of the civic and adminis-
trative life of the nation,

(ii) of the regulation of socio-religious life of the
people.

In ancient and medieval times, society, state and
church were intermingled, and the same calendar
served all purposes. The modern tendency is to
dissociate civic life and administration from socio-
religious life. Also due to the enormous growth of
intercourse amongst all nations of the world, the need
has been felt for a World Calendar dissociated from
all religious and social bias. Owing to historical
reasons, the Gregorian calendar is now used inter-
nationally for civic and administrative purposes, but
it is very inconvenient, and proposals have been made
to the U. N. O. for the adoption of a simple World
Calendar (vide § 2.7).

1.4 SUBDIVISIONS OF THE DAY

For pactical prurposes, the day is divided into 24
hours, an hour into sixty minutes and a minute into
sixty seconds.

1 mean solar day « 24 x 60 x 60 = 86, 400 seconds.

The subdivisions of time are measured by highly
developed mechanical contrivances (clocks, watches
and chronometers), but they have come into use only

during comparatively recent times. The ancient people
used very primitive devices.

The time-keeping apparatus of the ancients were
the gnomon, the sundial, and the water-clock or the
clepsydra. The first two depend on the motion of the
sun, and require correction. The water-clock which
probably was first invented in Egypt, appears to have
been used down to the time of Galileo, when the
discovery of pendulum motion 1 led to the invention of
clocks based on pendulum motion or use of the balance
wheel.

Subdivisions of time can be measured by the motion
of any substance, which repeats itself regularly ; at the
present time in addition to pendulum clocks, quartz-
clocks, and ammonia clocks have been used. The
latter depend upon harmonic motions within the
ammonium molecule, giving rise to spectral lines whose
frequency can fcfe accurately measured.

The present divisions of the solar day have
interesting history.

It is stated by Sarton that the ancient Sumerians
(original dwellers of Babylon) divided the day-time and
night-time into three watches each. The watches
were naturally of unequal lengths and varied through-
out the year. It was only during equinoxes that the
watches were of equal length, each of our 4 hours.

These unequal watches continued down to medieval
times. The life of a medieval monk was watch-wise as
follows.

(1) Matins— last watch of the night. The monk

got up nearly two hours before sun-
rise and started his work,

(2) Prima— at sunrise,

(3) Tertia — half-way between sunrise and noon-

time of saying Mass,

(4) Sexta— at noon (hence the word, Siesta-

midday rest),

(5) Nona— mid-afternoon, whence our word Noon,

(6) Vespers— an hour before sunset,

(7) Compline— at sunset.

The watches were variable in duration and in their
starting moments. Sarton remaks :

A clock regularly running and dividing the day into
periods of equal duration would have been, at first, more
disturbing than useful. For monastic purposes, a human
variable clock {e. g. a bell rung by a monk or lay brother
at the needed irregular intervals) was more practical than
an automatic one.*

But even in ancient times, the need for measure-
ment of equal intervals of time was felt. The ancient
Babylonians used the Nychthemeron (Day and Night

*Sarton, Introduction to the History of Science, Vol. Ill, Part I,
p. 716.

160

combined- JMrafro) into 12 hours of 30 Qesh each,
Qesh being -4 minutes. The Egyptians divided the day-
light time into 12 hours, and the night into 12 hours.
Later in medieval times, the 24-hour division for the
whole day (day and night) has been adopted. The
division into A.M. and P.M. were for the sake of
convenience, so that the maximum number of times a
bell has to be rung, on the completion of an hour,
would not exceed 12, for apparently ringing a bell 24
times would be a torture of the flesh.

The broad divisions of the day were secured by the
Hindus in two ways. They divided the day-time (from
sunrise to sunset) into 4 equal parts each called a
prahara or yama. The night time was also similarly
divided into 4 equal praharas. The prahara is so
popular a unit in Indian time measurement that even
the lay man expresses time in terms of praharas and
half praharas. An alternative system of division of the
time is the 'muhurta' obtained by dividing the daytime
into 15 muhurtas determined by gnomon shadow
lengths The day muhurtas were measured from
lengths of shadows of the gnomon. The night muhurtas
ate similarly the fifteenth part of the night time.

As the durations of day and night are not equal
except on the vernal and autumnal equinox days, the
Prahara and muhurta of the day-time have not the
same durations as those of their nocturnal counterparts.
On equinox days, they are however equal, when

1 Prahara =3* <P-7* 30-
1 Muhurta =0 48 =2
The Hindu astronomers appear to have switched on
to the ahoratra during Vedariga Jyotisa times. As it is
rather complicated, we do not give an account of it.
The reader may consult Dixit's Bharatiya Jyohsastra.
But in Siddhanta Jyotisa, they had a full fledged
scientific system.

The scientific divisions of time followed by the
Siddhantas are the ghatika {davda or nadil prahara or
yama. and muhurta etc. The day is measured from
sunrise and the period from sunrise to next sunrise is
divided into 60 equal 'ghatika^ °* dan^as ; each ghatx
is subdivided into 60 vighatis or palas. and each mghaix
or pala into 60 vipalas. So a day consists of 60 >ghatis
or 3600 palas or 216000 vipalas. Thus
1 ghatika -24 m 0*.0
I pala - 24.0
1 vipala = 0.4

The pala or vighati is sometimes subdivided into 6
divisions called a prana. A prana is therefore equi-
valent to 4 sees, of time. There are 360 pranas in a
ghatjka and the day contains 360 x 60 or 21600 pranas,

REPORT OF THE CALENDAR REFORM COMMITTEE

the same as the number of minutes ( kola or lipiika ) in
a circle. In Siddhantas (astronomical treatises of the
Hindus) there are conceptions with nomenclatures of
still smaller divisions of time, but they had no practi-
cal utility.

None of the time-periods of the sun, and the moon,
m%. the year and the season, and the lunations and
half-lunations are integral multiples of the day ; on the
other hand, the figures run to several places of
decimals. How did the ancients, who quickly dis-
covered that the time-periods were not integral multi-
ples of the day, express their findings ?

It will take us a long dive into the history of
mathematical notation to elucidate this story. The
curious reader may consult Neugebauer's Exact Sciences
in Antiquity or van der Waerden's Science Awakening
(pp 51-61). In fact, the symbolism was very cumbrous
before the discovery of the decimal notation about
600 A.D. in India, where it quickly replaced the old
cumbrous notation. The discovery was quickly adopted
by the Arabs for certain purposes, but was first made
known to Europe by Leonardo of Pisa in a treatise on
Arithmetic published in 1202 A.D., but a few more
centuries passed before it was universally adopted.

The practice of expressing fractions by means of
decimals came later, both in India and Europe. In
India an astronomer who wrote an astronomical
treatise called 'Bhasvati* in 1099 A. D. was called
Satananda, (i.e. revelling in hundreds) because he
used to write fractions in hundredths i.e. i as 25
hundredths, f as 75 hundredths. In Europe, the
expression of fractions by decimals came into vogue
about the seventeenth century.

The Hindu astronomer of the Siddhantic age
expressed the periods of the sun, the moon and the
planets by the number of their periods in a Mahayuga
(4.32 x 10 6 years). The number is usually integral.
But how did this cumbrous system originate ?
Probably many of these values were obtained by
counting the number of days between a large number
of periods and dividing them by the number of periods.
For example, take the case of the length of the mean
lunation (lunar month). All ancient nations give
this length correct to a large number of decimals. This
must have been obtained by counting the number of
days between two new moons, separated by a large
number of years, and dividing it by the number of
lunations contained in the interval. Of course, the
utmost they could have done was to keep records for
at most a hundred years, but the rule of three was
always available.

In the following sections, the different ways of
tackling the calendar problem in different centres of

GENERAL PRINCIPLES OF CALENDAR MAKING

161

civilization have been described. We have described
in Chap. II, the purely solar calendars, in which the
moon is altogether discarded as a time-marker. This
practice originated in Egypt about 3000 B.C. These
calendars require only a correct knowledge of the
length of year, and are therefore comparatively simpler.
They required very little or almost no knowledge
of astronomy.

We have described in Chap. Ill, the luni-solar
calendars, prevalent in ancient Mesopotamia, India,
China and most other countries. In these calendars,
both the sun and the moon are used as time-markers,
and therefore precise knowledge of their motion in
the heavens was essential for the formulation of a
correct calendar. We mark two stages : first the
formulation of a calendar from a knowledge of only
the length of the year, and of the mean lunar
month. This was an older phase. It did not work
satisfactorily, because it depended on the mean motion
of the two luminaries. Actually, the time-predictions
have to be verified by actual comparison of the
predicted happenings (say of the vernal equinox
day in the case of the sun, or the first appearance
Of the crescent of the moon after new moon on the
western horizon) with the time of actual happenings.
This gave rise to the need for watching the daily
motion of the two luminaries, and invention of
methods for recording and storing these observations ;
in other words/ this led to the science of astronomy.
Early astronomy is almost completely calendarical.
At a later stage, the five planets attracted attention,
on account of their association with astrology.

We have therefore devoted Chap. IV to calendaric
astronomy, which was evolved by the Chaldeans and
taken over from them by the Greeks, and in time
diffused to other countries.

In Chap. V, we have described the various stages of
the development of the Indian calendar : — the empiri-
cal stage (Rg-Vedic), the mean motion stage ( Vedanga
Jyoti$a), and the scientific stsfge (Siddhanta Jyoti$a).
From 1200 A.D., astronomical studies became decadent
in India, and we have analysed the cause of decadence.
We have given a full account of precession, as most
Indian calendar makers still believe in the false theory
of Trepidation which disappeared from Europe after
1687 A. D.

1.5 AHARGANA OR HEAP OF DAYS : JULIAN DAYS

Though the Flux of Time is a continuous process,
it is divided for the sake of convenience and for
natural reasons too, into years, months and days.
The years are mostly counted from the beginning of
an era, so that if we wish to date a memorable event,

say the birth-day of George Washington, it can be
seen from an inspection of his birth register that it
took place on Feb.ll, of the year 1732. But this
practice by itself does not enable a scientific chrono-
logist to fix up the event unambiguously on the
absolute Scale of Time, unless the whole history of
the particular method of date-recording is completely
and accurately known One must know the lengths
of the individual months, the leap-year rules, and
the history of calendar reform. In the particular case
mentioned, though George Washington * according to
his birth register is stated to have been born on Feb.
11, 1732, his birth-day is celebrated on Feb. 22. Why ?
Because Feb. 11 was the date according to the Julian
calendar. But in 1752, England (America was then
a colony of England) adopted the reformed Gregorian
calendar, and by an Act of Parliament, declared Sept.
3 to be Sept. 14, a difference of 11 days. Following
the Gregorian calendar, Washington's birth-day had
to be shifted to Feb. 22. A scientific chronologist, say
of China, would find it difficult to locate Washington's
birth-day unless he knew the whole history of the
Gregorian calendar.

This difficulty is more pronounced when we
have to deal a luni-solar calendar, say that of Babylon.
Many records of lunar eclipses occuring in Babylon
were known to the Alexandrian astronomer, Claudius
Ptolemy, but they were dated in Seleucidean era, and
Babylonian months, say year 179, 10th of Nisan. Now
the Babylonian months were lunar, had lengths of 29
or 30 days, but the year could have lengths of 353, 354
383, 384 ( vide § 3'3 ). Therefore when two eclipse
datings were compared, it was impossible to calculate
the number of days between them, unless the investi-
gator had before him a record showing the lengths of
years and months between the two events. Ptolemy
expressed his datings according to the Egyptian calen-
dar, which enables one to calculate the interval far
more easily. He must have taken lot of pains to carry
out the conversion from the Babylonian to Egyptian
dates.

How much better it would have been if a great
genius at the beginning of civilization, say near about
3000 B.C., started with a zero day, and started the
practice of dating events by the number of days
elapsed since this zero date, to the date when this
particular event took place. Such a great genius did
not appear and a confusing number of calendars came
into existence. The scientific chronologist is now
faced with the reverse problem : Suppose two ancient
or medieval events are found dated according to two
different calendars. How to reduce these dates to an
absolute chronological scale ?

For this purpose, a medieval French scholar, Joseph
Scaliger introduced in 1582 A. D., a system known as

162

'Julian Days' after his father, Julius Scaliger. The

Julian period in years is

7980 years -19x28x15
19 being the length ia years of the Metonic Cycle,
- c „ of the Cycle of Indiction,

A O o , of the Solar Cycle,

and 28 » » » n »

It was found by calculation that these three cycles
started together on Jan. 1, 4713 B.C. So the Julian
period as well as the Julian day numbers started from
that date. The Julian period is intended to include all
dates both in the past and in the future to which refe-
rence is likely to be made and to that extent it has an
advantage over an era whose epoch lies within the
limits of historical time. The years of the Julian
period are seldom employed now, but the day of the
Julian period is frequently used in astronomy and
calendaric tables. Unlike the civil day, the Julian day
number is completed at noon.

Let us give the Julian days for a number of world-
events, asgivenbyGinzel, in his Eandbuch der Mathe-
matischm und Technischen Chronologic

REPORT OP THE CALENDAR REFORM COMMITTEE

Kaliyuga
Nabonassar
Philippi
Saka era
Diocletian
Hejira
Jezdegerd
(Persian)
Burmese era
Newar era
Jelali era

Table 1 — Julian day numbers.
Date

... 17 February, 3102 B.C.
... 26 February, 747 B.C.
... 12 November, 324 B.C.
... 15 March, 78 A.D.
... 29 August 284 A.D.
... 16 July, 622 A.D.

Julian day

.. 588,465
1,448,638
1,603,398
1,749,621
1,825,030
1,948,440

16 June, 632 A.D. 1,952,063

21 March, 638 A.D. 1,954,167

20 October, 879 A.D. 2,042,405

15 March, 1079 A.D. 2,115,236

(Iran)

It may be mentioned here that the ideas underlying
continuous reckoning of days occurred much earlier to
the celebrated Indian astronomer, Sryabhata I (476-
525A.D.), who introduced it under the designation
''AharganJ* or heap of days in his celebrated Arya-
bha\\ya. The idea of counting ahar ^V^ or heaps of
days elapsed from a specified epoch upto the given date
dawned upon the Hindu astronomers as a necessity for
calculating the position of planets for that date. They
followed the cumbrous luni-solar calendar for dating
purposes, which was not based upon any simple rules.
It contains months of 29 or 30 days, and occasionally a
thirteenth month, the recurrence of which was deter-
mined by elaborate methods. The dates of the months
are not numbered serially, but designated by the
tithi current at sunrise. It was accordingly found
almost impossible to work out the mean positions of
planets on the basis of the luni-solar calendar alone.

For this purpose a continuous and uniform time scale
was necessary, and this was served by the ahargaQa.

Sryabhata had somehow the idea that the planets,
and the two nodes (which were treated as planets
in Hindu astronomy) return to the first point of Aries
after every 4.32 x 10 6 years, and there was a unique
assemblage of planets at the first point of the Hindu
sphere at some past date which he called the beginning
of Kali Yuga. The date assigned to the Kali beginning
is now known to be 3102 B.C., February 17-18. The
common period of revolution of planets of 4.32 x-10 6
years constitute a Mahayuga consiting of

Satya yuga of 1.728 x 10° years

Treta yuga of 1.296 x 10 6 "

Dvapara yuga of 0.864 x 10* "

Kali yuga of 0.432 x 10 6 "

Total 4.32 x 10 6 years

It may be noticed that

4.32 xl0 c ~ 12000 x 360

Sryabhata gave tables showing the number of
sidereal revolutions of planets . in the period of
4.32xl0 6 years. The total number of days in a
Mahayuga- 1,577,917,800 which gives the length of a
year = 365.25875 days.

Brahmagupta was evidently not satisfied that
Sryabhatas figures for the periods of planets were
correct. He introduced a Kalpa = 1000 Mahayugas -
4.32 xlO 9 years. The ' Kalpa was supposed to consti-
tute a 'Day of the Creator, Grand-father Brahma.
He gave the number of. sidereal revolutions of the
planets in a Kalpa, and thought he had improved
Sryabhatas figure for the year.

Brahmagupta s year = 365.25844 days.

Sryabhata calculated 'Ahargana' or heap of days,
from the beginning of the Mahayuga as the zero-day.

But evidently this practice involves very large
numbers, and is inconvenient to use. Therefore the
later astronomers used modifications of the system
by counting Ahargaw from other convenient epochs,
within historical reach. The different epochs which
have been used are : —

(1) The beginning of the Kali era or 3102 B.C.

(2) 427 Saka era or 505 A.D. as is found in
FaftcasiddhanUka of Varahamihira.

(3) 587 Saka era or 665 A.D. as is found in the
Kha^iakhUyaka of Brahmagupta.

(4) 854 Saka era or 932 A.D, as is found in the
Laghurn&nasa of Muiijala.

(5) 961 Saka era or 1039 A.D. in the Siddhftnta
Sehhara of Srlpati.

The astronomical treatises of the Hindus have been
divided into three categories according to the initial

GENERAL PRINCIPLES OF CALENDAR MAKING

163

epoch employed for calculation. In which the calcula-
tions of ahargay,a as well as the planetary mean places
are made from the Kalpa, is called a Siddhanta ; when
the calculations start from a Mdhayuga or Kali'
beginning it is called a Tantra, and when it is done
from a recent epoch it is called a Karaw. In any
case, the mean places of the planets with their nodes
and apsides are given for the epoch of the treatise
from which calculations are to be started, with rules
for finding the aharga^a for any later date. This
ahargaya is then made use of in finding for that later
date the positions of planets from their given initial
positions and their daily motions, for,

The mean position at any epoch

= the mean position at the initial epoch

+ daily motion x ahargana.
Due to the complexity of the Hindu luni-solar
calendar, one has to go through complicated rules in
determining the ahargaria for any particular day.
Dr. Olaf Schmidt of the Brown University and the
Institute of Advanced Study, in discussing the method
of computation of the Aharga<$a at length, has pointed
out that the present Hindu method suffers from a

disturbing discontinuity. The curious reader may go>
through his article published in the Centaurus.

We, however, give below the corresponding Julian
day numbers and Kali ahargana for certain modern
dates.

Julian days

(elapsed at
mean noon)

2,415,021
2,432,413
2,435,554

Kali ahargaipa
(elapsed at
following midnight)

1,826,556
1,843,948
1,847,089

1900, Jan. 1
1947, Aug. 15
1956, Mar. 21

The difference between the two numbers 588,465
represents the Julian day number on the Kali epochs
as already stated.

The use of ahargana plays a very important part in
modern epigraphical researches when the date recorded
in an inscription is required to be converted into the
corresponding date of the Julian calendar. If the
Kali aharga<$a for the recorded date can be determined,
then the problem of ascertaining the corresponding.
Julian or Gregorian date becomes a very easy task.

CHAPTER II

The Solar

2.1 TIME-RECKONINGS IN ANCIENT EGYPT

Like other nations of antiquity the early Egyptians
had a year of 360 days divided into 12 months, each
of 30 days ; but they found very early from the
recurrence of the Nile flood, that the seasonal year
consisted approximately of 365 days, and that a month
or lunation (period from one new-moon to another)
was nearly 29| days (real length 29.531 days). But
they had already framed a calendar on the 30-day
month, and 360-day year, which had received religious
sanction. Hence arose the first necessity for calendar-
reform recorded in ancient history. To persuade the
people to agree to this reform their priests invented
the following myth :

"The Earth god Seb and the sky goddess Nut had once
illicit union. The supreme god Ra, the Sun, thereupon
cursed the sky goddess Nut that the children of the
union would be born neither in any year nor in any month.
Nut turned to the god of wisdom, Thoth, for counsel. Thoth
played a game of dice with the Moon-goddess, and won
from her y^th part of of her light out of which he made
five extra days. To appease Ba the Sun-god, these five
days were given to him, and his year gained by five days
while the Moon-goddess's year lost five days. The extra
five days in the solar year were not attached to any month,
which continued to have 30 days as before ; but these days
came at the end of the year, and were celebrated as the
birthdays of the gods born of the union of Seb and Nut,
viz., Osiris, Iais, Nephthys, Set and Anubis, five chief gods
of the Egyptian pantheon." *

Let us scrutinize the implications of this myth.
This is tantamount to discarding the moo?i altogether as a
time-maker, and basing the calendar entirely on the sun.
This was a very wise step, for as has been found from
ancient times, the moon is a very inconvenient time-
marker. The Egyptians maintained the old custom
of keeping months of 30 days' duration, and 12 months
made a year. But five days (Epagomenai in Greek) were
added to the year at the end, which were not attached
to any month. They were celebrated as national
holidays. Each month of the Egyptian calendar was
divided into 3 weeks, each of 10 days (Decads).

The names of the Egyptian months together with
the dates of beginning of each month as they stood in
22 B.C., are as follows :

* Zinner— Qeschichte der Sternkunde, p. 3,

Calendar

Egyptian Calendar

Julian Calendar

1 Thoth

(30)

29 August

1 Phaophi

(30)

d,o September

1 Athyr

(30)

28 October

1 Choiak

(30)

27 November

1 Tybi

(30)

27 December

1 Mechir

(30)

26 January

1 Phamenoth

(30)

25 February

1 Pharmuthi

(30)

27 March

1 Pachon

(30)

26 April

1 Payni

(30)

26 May

1 Epiphi

(30)

25 June

1 Mesori

(30)

25 July

(1 Epagomenai 5)

24 August

The year was divided into three seasons, each of
four months : Flood time, Seed time and Harvest time.

But the Egyptians soon found that even a year of
365 days did not represent the correct length of the
year, which, as we now know, is nearly 365J days.
This fact they appear to have discovered in two
different ways :

(1) from their measurement of the length of the
year from heliacal risings of Sirius, and

(2) from their long record of floods extending
over centuries.

The fixed star Sirius, which is the most brilliant
star in the heavens, was early associated with the chief
goddess of the Egyptian pantheon, Isis> and was the
subject of observation by her priests. The day of its
first appearance on the eastern horizon at day-break
(heliacal rising) appeared to have been carefully
observed, and then on every subsequent day, its posi-
tion in the sky at sunrise used to be noted. It was
found that gradually it got ahead of the sun, so its
appearance on the horizon would be observed sometime
before sunrise, and on every successive sunrise, it
would be found higher up in the heaven. After about
a year it would be seen in the western horizon at
sunset for a few days till it could no longer be traced.
The Egyptians found as a result of long periods of
observation, that it came again to the horizon at day
break at the end of 365^ days, not 365 days. If on one
year, the heliacal rising of Sirius took place on Thoth 1,
(Thoth was the name of the first month of the year)
four years later it would take place on Thoth 2, and
forty years later on Thoth 11. As the mean interval

THE SOLAB CALENDAB

165

of heliacal rising of Sirius at the latitude of Memphis
was 365.25 days, the Egyptians concluded that the
heliacal rising of Sirius would continue to move round
the year in a complete cycle of ecu 1460 years ; called
the Sothic cycle, after Sothis (Isis). They also appear
to have found from observations over long periods of
years that the Nile flood occurred not at intervals of
365 days, but of 365^ days.

On account of the deficiency of i day in the year,
the year-beginning lost touch with the arrival of the
Nile flood, though the temple priests had devised a
method of finding out the interval between Thoth 1,
and arrival of the Nile flood by observations of the
heliacal rising of the bright star Sirius, identified with
their chief goddess Isis. But they kept the knowledge
to themselves.

If the Egyptians carried out a reform of their calen-
dar incorporating this fact, that the tropical year had a
length of 365* days, their calendar could have been
almost perfect. All that they had to do teas to take 6
extra days instead of 5 every fourth year. But the 365-
day year had so much soaked into the Egyptian mind,
that this move for calendar reform was never adopted
inspite of serious attempts by earlier Pharoahs, and
later, a more serious one by the Graeco-Egyptian
ruler Ptolemy Euergetes ( 238 B.C. ). But it became
generally known that the correct length of the year
was 365^ days. Fotheringham in his article on 'The
Calendar" observes :

An additional day was inserted at the close of the
Egyptian year 23-22 B.C. on August 29 of what we call the
Julian calendar, and at the close of every fourth year after-
wards, so that the reformed or Alexandrian year began
on August 30 of the Julian calendar in the year preceding
a Julian leap year and on August 29 in all other years.
The effect of this reform was to keep each Egyptian
month fixed to the place in the natural year which it
happened to occupy under the old calendar in the years
2G-22 B.C. But the old calendar was not easily suppressed,
and we find the two used side by side till A.D. 238 at least.
The old calendar was probably the more popular, and
was preferred by astronomers and astrologers. Ptolemy
(150 A.D.) always used it, except in his treatise on annual
phenomena, for which the new calendar was obviously more
convenient. Theon in the fourth century A.D., though
mentioning the old calendar, habitually used the new.

Though not quite perfect, the Egyptian calendar
was greatly admired in antiquity on account of its
simplicity, for the length of the year and the months
were fixed by definite rules and not by officials or
pandits. The religious observances fell on fixed days
of the month and at stated hours, which were fixed
about 1200 B.C.

On account of its simplicity, the Egyptian calen-
dar was adopted by many nations of antiquity, and
even sometimes by the learned Chaldeans and Greeks,.
Fotheringham observes :

"The Egyptian calendar was, upto the time of Julius-
Caesar's reform of the Roman calendar in 46 B.C., the only
civil calendar in which the length of each month and of
each year was fixed by rule instead of being determined by
the discretion of officials or by direct observation. If the
number of years between two astronomical observations,
dated by the Egyptian calendar, was known, the exact
number of days could be determined by a simple calculation.
No such comparison could be made between dates referred
to any other civil calendar unless the computer had access
to a record showing the number of days that had actually
been assigned to each month and the number of months that
had actually been assigned to each year. It is true that the
Egyptians did not use a continuous era, but were content to
number the years of each reign separately, so that there was.
a difficulty in identifying a particular year, but the astronomers
of the Ptolemaic age rectified this by the introduction of
eras.* The simplicity and regularity of the Egyptian
calendar commended it to astronomers, who found it
excellently adapted to the construction of tables that could
be readily applied and used even for a remote past or for
a distant future without any fear that the system by which
time was reckoned in the tables might not coincide with the
system in actual use. In the second century B.C. we find
Chaldean observations, sometimes nearly six centuries old,
reduced to the Egyptian calendar in the works of
Hipparchus (126 B.C.), who observed not in Egypt but at
Ehodes, and cited from him by the Egyptian Ptolemy in
the second century of our era ; we also find in the second
century B.C., an Athenian observation of 432 B.C. reduced
to the Egyptian calendar oh an inscription found at Miletus,
which appears to represent the work of the astronomer
Epi genes", t

This calendar survives in a slightly modified form
in the Armenian calendar, the three first months of
the old Egyptian year corresponding exactly with the
three last months of the Armenian year. The
Alexandrian calendar is still the calendar of Abyssinia
and of the Coptic Church, and is used for agricultural
purposes in Egypt and other parts of northern Africa.

2.2. SOLAR CALENDARS OF OTHER ANCIENT NATIONS

The story of the calendar in Egypt has been given
in full, because the ancient Egyptians evolved a very
. simple and convenient calendar which, as mentioned
before, would have been almost perfect (provided the
year was taken to consist of 365J days instead of 365
days). This was rendered possible by their bold initia*

* The Nabonassar Era— vide § 3.4.

+ Article on *The Calendar', Nautical Almanac, 1935. ,

166

REPORT OF TflE CALENDAR REFORM COMMITTEE

tive of discarding the moon as a time-marker. But
people in the remaining parts of the civilized world
(e.g., in Babylon, Greece, India and China) in ancient
and moderm times, retained tne moon and preferred
the more complex luni-solar calendars described
in Chap. III. This was rather fortunate, for if their
rulers had adopted the Egyptian calendar, the priest-
astronomers of ancient nations, particularly of
Babylon, would never have taken to observation
of the sun, the moon, and the planets, and tried
to evolve mathematical formulae for predicting their
positions amongst stars in advance (the Ephemerides)
which form the basis on which our astronomical
knowledge has been built up ; for the Egyptian
calendar was evolved simply from results of
experiences extending over centuries, and required
almost no astronomical sense, or observations either
of the sun, the moon and stars, except the heliacal
rising of Sirius. It was simple and convenient, but
like many perfect things, it killed intellectual curiosity.

But as will be described in Chap. Ill, the luni-solar
calendar is a very complex thing, and has taken in-
finite variations in different regions. Hence the
simple Egyptian calendar appealed to many nations
of antiquity as well as of modern times. We have
related the case of the Greek astronomers Hipparchos
and Ptolemy who preferred the Egyptian method of
date-recording to the Greek methods. This was,
however, not the solitary instance.

2.S THE IRANIAN CALENDAR

The great Iranian conqueror Darius (520 B. C),
whose empire comprised Egypt, Mesopotamia, Syria
and Asia Minor, besides his native country of Iran,
certainly came into contact with the diverse calendars
of older civilizations, but he appears to have preferred
the Egyptian calendar to the more complex Babylo-
nian calendar, and introduced it in his vast empire.

But the astronomers of Darius made correction of
the deficit of i day of the year in another way.
They had all years of 365 days, but used an interac-
lary month of 30 days in a cycle of 120 years.

All the names of the old Iranian months and
details of their calendar are not available now. The
month-names as far as could be traced are stated
below : —

1. Thuravahara

2. Thaigraci

3. Adukani
4

5. Garmapada
6

7. Bagayadi

9. Atriyadija

10. Anamaka

11. Margazana

12. Viyachna

The Persians did not have weeks or decads, but
named * the successive days of the month serially
according to their gods or religious principles, as
below : —

Zend

Pehlewi

Nearest Vedic

1. Ahurahe mazdao

AGharmazd

2. Vanheus mananho

VohGman

3. Ashahe vahistahe"

Ardavahisht

4. Kshathrahe vairjghe* Shatvalro

O. opeiltd.J<HJ cini.ia.njio

Spendarmad

6. Haurvatato

Horvadad

7. AmeretatO

Amerodad

Amrtatva

8. Dathusho

Dln-i-pavan AtarO

9. SthrO

StarO

Atharvan

10. Apam

Svan

Apam

11. Hvarekshaetahe*

Khurshgd

12. Maonho

Mah

13. Tistrjehe-

Tlr

14. Geus

Gosh

15. Dathusho

Dln-i-pavan Mitro

16. Mithrahe*

Mitro

Mitraha

17. Sraoshahe

SrOsh

18. Rashnaos

RashnQ

19. Fravashinam

Fravardln

20. Verethraghnahe

Vahram

Vrtraghnaha

21. RamanO

Ram ^

22. Vatahe

Vad

23. Dathusho

Din-i-pavan DinO

24. Daenajao

Dlno

25. Ashois

Ard

26. Arstato

Sshtad

27. AsmanO

5sman

28. ZemO

Zamjad

29. Mathrahespentahe*

Marspend

30. Anaghranam

Aniran

After the Islamic conquest of Persia

in 648 A.D.,

the purely lunar calendar of Islam (Hejira) was
imposed on Persia, but it does not appear to have
been liked by the native Iranians.

In 1074-75 the Seljuq Sultan Jelal Uddin Melik
Shah called upon the celebrated Omar Khayyam and
seven others to reform the old Persian calendar.
The calendar as reformed by them was called Tarikh-
i-Telali, its era was the 10th Ramadan ^ of Hejira

THE SOLAR CALENDAR

167

471- 16th March, 1079 A.D. There are many
interpretations of the Jelali reform, the modern
interpretation being 8 intercalary days in 33 years,
giving the length of the year as 365.24242 days. The
year started from the day of or next to vernal equinox.

The Parsees in India, the followers of the Prophet
Zarathustra are the descendants of Iranians who took
shelter in India on the. conquest of Persia by the
Arabs. The following details about their calendar
is reproduced from Encyclopaedia Britannica (14th
edition), Parsees : —

The Parsees of India are divided into two sects, the
Shahanshahis and the Kadmis. They differ as to the correct
chronological date for the computation of the era of
Yazdegerd, the last king of Sassanian dynasty, who was
dethroned by the caliph Omar about A.D. 640. This led to
the variation of a month in the celebration of the festivals.
The Parsees compute time from the fall of Yazdegerd. Their
calendar is divided into twelve months of thirty days each ;
the other five days, being added for holy days, are not
counted. Each day is named after some particular angel of
bliss, under whose special protection it is passed. On feast
days a division of five watches is made under the protection
of five different divinities. In midwinter a feast of six days
is held in commemoration of the six periods of creation.
About March 21, the vernal equinox, a festival is held in
honour of agriculture, when planting begins. In the middle
of April a feast is held to celebrate the creation of trees,
shrubs and flowers. On the fourth day of the sixth month
a feast is held in honour of Sahrevar, the deity presiding
over mountains and mines. On the sixteenth day of the
seventh month a feast is held in honour of Mithra, the deity
presiding over and directing the course of the sun, and also
a festival to celebrate truth and friendship. On the tenth
day of the eighth month a festival is held in honour of
Farvardin, the deity who presides over the departed souls of
men. This day is especially set apart for the performance
of ceremonies for the dead. The people attend on the hills
where the *' towers of silence" are situated, and in the sagris
pray for the departed souls. The Parsee scriptures require
the last ten days of the year to be spent in doing deeds
of charity.

In modern Iran when Riza Shah Pahlavi came to
power in 1920, he instituted a reform of the existing
Muslim calendar abandoning the strictly lunar
reckoning and introducing purely solar year restoring
the early Persian names which had never fallen
entirely out of use.

The names of the months, and their lengths are
as follows :

Parvardin-mah (31) begins 21 or 22 March
Ardibahisht-mah (31) „ 21 or 22 April
Khordad-mah/{31) „ 22 or 23 May

Tir-aiah (31) M 22 or 23 June

Mordan-mah (31)
Shartvar-mah (31)
Mehr-mah (30)
Aban-mah (30)
Azar-mah (30)
Dai-mah (30)
Bahman-mah (30)
Esfand-mah (29, 30)

begins 23 or 24 July

23 or 24 August
23 or 24 September
23 or 24 October
22 or 23 November
22 or 23 December
21 or 22 January
20 or 21 February

2.4 THE FRENCH REVOLUTION CALENDAR

The Egyptian calendar attracted the notice of
the calendar committee of the French Revolutionary
Government (1789-1795) who wanted to replace
Religion by Reason. The committee consisted, amongst
others, the great mathematicians Laplace and Lagrange
and the poet d'Eglantine. Laplace proposed that the
year 1260 A.D,, when according to his calculations the
equinoctial line ivas perpendicular to the apse line of
the Earth's orbit should be taken the starting point of
the French Revolution Era in place of a hypothetical
year of Chrisfs birth. But the calendar committee
did not agree with him but started the era of the
glorious French revolution, with the autumnal
equinox day of 1792 A.D., as this was nearest in date
to the outbreak of the revolution. Sentiment proved
stronger than cold scientific reasoning.

French Revolution Calendar

( 1792 Sept. 22 to 1806 )
( The Months consist of 30 days each )

Month

Vendemiaire
Brumaire :
Frimaire :

Nivose :
Pluviose :
Ventose :

7. Germinal

8. Floreal :

9. Prairial :

Season
AUTUMN

Grape gathering

Fog

Frost

WINTER

Snow

Rain

Wind

SPRING
Seed
Blossom
Pasture

Month beginning

Sept. 22
Oct. 22
Nov. 21

Dec.
Jan.
Feb.

21
20
19

10. Messidor :

11. Thermidor

12. Fructidor :

Day of Virtue
„ Genius
„ Labour
„ Opinion
„ Rewards

SUMMER

Harvest
Heat
Fruit

March 21
April 20
May 20

June 19

July 19

Aug. 18

Sept. 17

* 18

,, 19

■» 20.

« 21

168

REPORT OF THE CALENDAR REFORM COMMITTEE

The seven-day week was abandoned for a week of
10 days. The month names were invented by the poet
member of the committe. The last five days were
dedicated to the service of the poor ( Sans-Culottides )
and did not form part of any month.

After 13 years of service, the French Revolution
calendar was abolished by Napoleon Bonaparte, then
emperor of France, as part of his bargain with the
Roman Catholic Church for his coronation by the Pope.

2.5 THE ROMAN CALENDAR

(The Christian Calendar)

What is now known as the Christian calendar, and
used all over the world for civil purposes, had originally
nothing to do with Christianity. It was, according to
one view, originally the calendar o£ semi-savage tribes
of Northern Europe, who started their year sometime
before the beginning of Spring (March 1 to 25) and had
only ten months of 304 days ending about the time of
winter solstice (December 25), the remaining 61 days
forming a period of hybernation when no work could
be done due to the onset of winter, and were not
counted at all. The city state of Rome also had
originally this calendar, but several corrections were
made by the Roman Governments a -^t epochs

and the final shape was given to it by Julius Caesar in
46 B:C ; the calendar so revised is known as the Julian
calendar.

As already stated, this calendar originally had
contained ten months from March to December
comprising 304 days. It may be regarded as certain
that the months were lunar. The second Roman king
of the legendary period, Numa Pompilius, is supposed
to have added two months (51 days) to the year in
about 673 B.C., making a total of 355 days ; January
(named from the god Janus, who faced both ways) now
began the year, and February preceded March, which
became the third month. The number of days of the
months were 29, 28, 31, 29, 31, 29, 31, 29, 29, 31, 29, 29.
Adjustment of the year to the proper seasons was
obtained by intercalation of a thirteenth month of
actually 22 or 23 days* length (called Mercedonius)
after two years or three years as was considered nece-
ssary, and was inserted between February and March.*
Had the intercalation been applied regularly at alter-
nate years the additional days in four years would
have been 45 (22 + 23) or Hi days per year on average,

* Id fact, the intercalary month consisted sometimes of 27 day $
and sometimes of 28 days and was inserted after February 23. Th
last five days of February, which were due to be repeated after ti i
close of the intercalary month, were not actually repeated, result -h-.g
in the intercalation of 22 or 23 days only.

and so the year-length would have been 366£ days,
only one day in excess of the correct length. But as
the intercalation was applied tather arbitrarily some-
times after two years and sometimes after three years,
the year-beginning gradually bhifted and the year
started before the arrival of the proper seasons.

The days of the month in the Roman calendar were
enumerated backwards from the next following Kalends (1st
of month), Nones (5th of month, except in the 31-day months,
when the 7th of month), or Ides (13th of month, except in
the 31 -day months, when the 15th of month). Ihe day
after the Ides of March, for instance, would be expressed as
17 days before the Kalends of April.

The Romans upto 45 B.C. apparently had rather
a vague idea of the correct length of the year.
Julius Caesar after his conquest of Egypt in 44 B. C.
introduced the leap-year system on the advice of
Egyptian astronomer Sosigenes, who suggested that
the mean length of the year should be fixed
at 365i days, by making the normal length of the
year 365 days and inserting an additional day every
fourth year. At the same time the lengths of the
months were fixed at their present durations. The
extra day in leap years was obtained by repeating the
sixth day before the Kalends of March. The name
Quintilis, the 5th month from March, was changed to
July (Julius) in 44 B.C. in honour of Julius Caesar, and
the name Sextilis was changed to August in 8 B.C.
during the reign of his successor, Augustus, and in
honour of him. There is a very widespread idea that
the durations, of July and August were fixed at 31 days
each in order to please 1 the two Roman dictators
Julius Caesar, and Octavious Caesar, also called
Augustus, and for this purpose the two extra days were
cut off from February, thus reducing its duration to
28 days. It is a nice story, but does not appear to
have been critically probed.

Owing to the drifting of the year-beginning, the
year 46 B.C. started about 90 days before the proper
seasons. The months were first brought back to their
correct seasons by giving the year corresponding to
46 B.C., a normal intercalation of 23 days after February
and then inserting 67 additional days between
November and December. This year therefore contai-
ned 445 days in all and is known as the 'year of
confusion.

But the perfect calendar was still a long way off.
Caesar wanted to start the new year on the 25th
December, the winter solstice day. But people resisted
that choice because a new-moon was due on January 1,
45 B.C. and some people considered that the new-moon
was lucky. Caesar had to go along with them in their
desire to start the new reckoning on a traditional lunar
landmark.

THE BOLAB CALENDAR

169

The Julian calendar spread throughout the Roman
empire and survived th$ introduction of Christianity.
But the Christians introduced their c^wn holidays
which were partly Jewish in origin and for, this, luni 4 -
solar and week-day reckonings had to be adopted.

Origin of the Seven-day Week

Historical scholarship has shown that unlike, the
year and the month, the seven-day week is an artificial
man-made cycle. The need for having this short
cycle arose out of the psychological need oi mankind
for having a day of rest and religious service after
protracted labour extending over days. The seven-day
week with a sabbatical day at the end, or something
similar to it, is needed not only by God Almighty, but
also by humbler toiling men. But there has been no
unanimity of practice.

As already stated, the ancient Egyptians had a ten-
day week. The Vedic Indians had a six-day week
The ancient Babylonians who started the month on the
day after new-moon, had the first, eighth, fifteenth,
and the twenty-second day marked out for religious
services. This was a kind of seven-day week with
sabbaths, but the last week might be of eight or nine
days' duration, according as the month which was
lunar had a length of 29 or 30 days. The ancient
Iranians had a separate name for each day of the
month, but some days, at intervals of approximately
seven, were marked out as Din-i-Parvan, for religious
practices. The pattern followed appears to have been
similar to the Babylonian practice. The continuous
seven-day week came into general use sometime after
the first century A.D. It was unknown to the writers
of the New Testament who do not mention anything
about the week day on which Christ was crucified or
the week day on which he is alleged to have ascended
to Heaven. The fixing of Friday and Sunday for these
incidents is a later concoction, dating from the fifth
century after Christ. All that the New Testament
b(Qoks say is, that He was crucified on the day before the
Hebrew festival of Passover which used to be celebrated
and is still celebrated on the full-moon day of the
month of Nisan.

The continuous seven-day week was evolved on
astrological grounds by unnamed astronomers who
may have been Chaldean or Greek at an unknown
epoch, butbefore the first century A.D. The Jews
ad&pted it as a cardinal part of their faith during
days of their contact with the Chaldeans. It is not their
invention. We give a short story of this invention, as
it is generally believed. But it may riot be quite
accurate in all details.

Invention of the Seven- day Week

Much of ancient astronomical knowledge is due to
Chaldean astronomers who flourished between the
seventh century B.C. and the third century A.D., as
related in §4*7. They gave particular attention to the
study of the movement of the sun, the moon and
the planets, which they identified with their gods,
because they thought that destiny of kings and states
were controlled by the gods, i.e., by the planets,
and attached the greatest importance to the observa-
tion of the position and movement of planets. They
attached magical value to the number 'Seven' which
was the number of planets or gods controlling human
destiny.

In 'Planetary Astrology', the sun, the moon and
the five planets, were identified with the chief gods of
the Babylonian pantheon^as given below :

Planets Babylonian

God-names

Iheir function

(1)

Saturn .

. . .Ninib

God of Pestilence and

Misery.

(2)

Jupiter.

. .Marduk , . .

King of Gods.

(3)

Mars

Nergal . . .

God of War.

(4)

Sun , .

Shamash . . .

God of Law & Order or

Justice.

(5)

Goddess of Fertility.

(6)

God of Writing.

(7)

God of Agriculture.

These seven gods, sitting in solemn conclave, were
supposed to control the destinies of kings and
countries, and it was believed that their will and
judgement with respect to a particular country or its
ruler could be obtained from an interpretation of the
position of the seven planets in the heavens, anfl the
nature of motion of the planets (direct or retrograde).

The Chaldean god-names are given in the second
column, and the functions they control in the third
column. Their identification with the Roman gods .is
given in the first column. The planets* * were put
in the order o^ their 'supposed distances from .the earth.

Further, the day was divided into 24 hours, and
each of the seven gods was supposed to keep watch
on the world over each hour of the day in rotation.
The particular day was named after the god who
kept watch at the first hour. Thus on Saturday, the
watching god on the first hour was Saturn, and
the day was named after him. The succeeding

♦Planets used nol in modern sense but m the old sense of & tvavderr
ing heavenly body.

170

REPOBT OF THE CALENPAB REFORM COMMITTEE

hours of Saturday Were watched by the seven gods
in rQtation as- follows :~

Saturday

Hours 12 3 4 5 6 7 8.. .14 15 22 23 24 25

God Watching 1 2 3 4 5 6 7 1... 7 1 1 2 3 4 (Sun)
The table shows the picture for Saturday. On
this day, Saturn keeps watch at the first hour, so the
day is named after him. The second hour is watched
over by (2) Jupiter, third by (3) Mars and so on.
Saturn is thus seen to preside at the 8th, 15th and
22nd hours of Saturday. Then for the 23rd, 24th and
25th hours come in succession (2) Jupiter, (3) Mars
and (4) Sun. The 25th hour is the first hour of the
next . day, which was accordingly named after the
presiding planet of the hour, vwr M No. 4 which is
Sun. We thus get Sunday following Saturday. If
we now repeat the process, we get the names of the
week days following each other, as follows .

Saturday, Sunday, Monday, Tuesday,
Wednesday, Thursday, and Friday.

Saturn

C Moon

Fig. 1— The order of week-days derived from the order of planets.
Saturday followed by Sunday, then Monday and so on.

The Jews, it may be mentioned*, reckon the days
by ordinal numbers— the first, seconds seventh
day. The "first day is Saturday. V '

The seven-day week, from the account of its origin
is clearly based on astrological ideology. The conti-
nuous seven-day week was unknown to the classical
Greeks, the Romans, the Hindus, and early Christians.
It was introduced into the Christian world by an edict
of the Roman emperor Constantine, about 323 A.D.,
who cbanged the Sabbath to the Lord's Day (Sunday),
the week-day next to the Jewish Sabbath. Its
introduction into India is about the same time and
from the same sources. The week-days are not
found in earlier Hindu scriptures like the Veda s or

the classics like the great epic Mahabharata. They
occur in inscriptions only from 484 A.D., but not in
inscriptions of 300 A.D. Even now, they form but an
unimportant part in the religious observances of the
Hindus which are determined by the moon s phases.

It can therefore be said that the unbroken seven-
day week was not a part of the religious life of any
ancient nation, and it is not, even now, part of the
religious life of many modern nations. It is a man-made
institution introduced on psychological grounds, and
therefore can be or should be modified if that leads
to improvement and simplification of human life.

The Christian Era

The present Christian era came into vogue much
later. About 530 A.D., the era-beginning was fixed
from the birth year of Christ which was fixed after
a certain amount of research by the Scythian Bishop
Dionysius Exiguus and Christ's birth day (Christmas)
was fixed on December 25 which was the Julian date
for the winter solstice day and the ceremonial birth
day of the Persian god Mithra in the first century B.C.
The discovery of a Roman inscription at Ankara shows
that King Herod of the Bible who is said to have
ordered the massacre of innocents was dead for four
years at 1 A.D., and therefore Christ must have been
born on 4 B.C., ox somewhat earlier.

2.6 THE GREGORIAN CALENDAR

The Julian year of 365.25 days was longer than
the true year of 365.2422 by .0078 days, so the winter
solstice day which fell on December 21 in 323 A.D. f
fell back by 10 days in 1582 A.D. and the Christmas
day appeared to be losing all connections with the
winter solstice. Similar discrepancy was also noticed
in connection with the observance of the Easter.*
Various proposals were made for correcting the
error and the Council of Trent which assembled in
1545 authorised the Pope to deal with the matter.
When in 1572, Gregory XIII became Pope, these
schemes were considered and the plan that was most

* Easter, the^nost joyous of the Christian festivals, is observed
annually throughout Christendom in commemoration of the resurrec-
tion of Jesus Christ, on the first Sunday after the full-moon
following the vernal equinox day. The last days of Christ coincided
with the Passover fast of the Jews and his death fell upon the day
of the feast of the Passover, on the 14* day of the month of Nisan.
As the date of Easter is associated with the moon's phased as well
as the vernal equinox day, it is a movable festival, falling anywhere
between March 22 and April 25. A movement is going on for
narrowing down the range of variation of the Easter day ; m 1928
the British Parliament passed the Easter Act, which contingent
upon its acceptance internationally, fixed Easter day as the first
Sunday after the second Saturday in April, falling between April
9 and 15. {Vide Encyclopaedia Britannica> Easter).

THE SOLAE CALENDAR

171

favoured was the one that had been proposed by
Aloysrus Lilius, a Neapolitan physician. In 1582, Pope
Gregory XIII published a bull instituting the revised
calendar and ordained that Friday, October 5 of that
year was to be counted as Friday, October 15. For
the future, centurial years that were not divisible by
400 were not to count as leap-years ; in consequence
the number of leap-years in 400 years was reduced
from 100 to 97 and the year-length of the calendar
thus became 365*2425 days, the error being only one
day in 3300 years.

The Gregorian reformation of the calendar was
at once adopted by the Catholic states of Europe,
but other Christian states took longer time to accept
it. In Great Britain it was officially introduced in
1752. As the error had by that time amounted to
11 days, the September of 1752 was deprived of these
days and 3rd September was designated as the 14th
September. In some countries the Gregorian calendar
was not adopted until the present century. China
and Albania adopted it in 1912, Bulgaria in 1916,
Soviet Russia in 1918, Roumania and Greece in 1924,
and Turkey in 1927. The rules for Easter which
were revised on the basis of the Gregorian calendar
have not been adopted by the Greek orthodox
Church.

Inspite of its wide use, the Christian or Gregorian
calendar is a clumsy and inconvenient system of time-
reckoning on account of the arbitrary length of its
months ranging from 28 to 31. With a view to
reforming it many schemes have been proposed, but
the one deserving of serious consideration is the new
World Calendar advocated originally by the Italian
astronomer Armellini in 1887 and adopted by the
World Calendar Association, Inc., which has its head-
quarters in New York (630, Fifth Avenue,, New York
20, N. Y), under the able presidentship of Miss
Elisabeth Achelis *

In the ecclesiastical calendar some holy days are
observed on fixed days of the year, others known as
movable festivals are observed on fixed days of the
week. Most of these are at fixed intervals before or
after Easter day. When the Easter day of any year
is fixed, the dates of other movable festivals can
accordingly be ascertained. The Council of Nice
convened in 325 A.D. adopted the rule for fixing the
date of Easter — it was to fall on the first Sunday after
the 14th day of the moon (nearly full moon) which
occurs on or immediately after March 21. In fact
there are certain special tables for determining the

* She had been devoting her services ungrudgingly for the
cause of calendar reform for the last twenty-five years, and also been
publishing a 'Journal of Calendar Reform* since then.

Easter day, based on the mean length of the lunar
month, and the determination does not require any
advance calculation of moon's position. The following
are the principal holidays dependent on the date of
Easter.

Days before Easter

Septuagesima Sunday 63

Quinquagesima „ 49

Ash Wednesday 46

Quadragesima Sunday 42

Palm Sunday 7

Good Friday 2

Days after Easter

Low Sunday 7

Rogation Sunday 35

Ascension Day 39

Whit Sunday 49

Trinity Sunday 56

Corpus Christi 60

2.7 THE WORLD CALENDAR

As already stated the Gregorian calendar is' a most
inconvenient system of time-reckoning. The days of
the months vary from 28 to 31 ; quarters consist of 90
to 92 days ; and the two half-years contain 181 and 184
days. The week-days wander about the month from
year to year, so the year and month beginnings may fall
on any week-day, and this causes serious inconvenience
to civic and economic activities. The number of
working days per month varies from 24 to 27, which
creates considerable confusion and uncertainty in
economic dealings and in the preparation and analysis
of statistics and accounts. The present Gregorian
calendar is therefore in dire need of reform.

The question of resolving these difficulties had
been under consideration for more than the last 100
years. In 1834, the Italian Padre Abbe' Mastrofini
proposed the Thirteen-Month Calendar, which was
strongly advocated by the positivist philosopher August
Comte. But this calendar could not attract much
attention and consequently it was abandoned. The
plan of reform which has received the most favourable
comments is, as mentioned earlier, that of the World
Calendar Association.

Let us explain the ideas behind this movement :

Calendars are used for regulating two essentially
distinct types of human activities, viz.,

(a) Civic and administrative,

(b) Social and religious.

In ancient and medieval times, different countries
and religions had developed their characteristic calen-
dars to serve both purposes, but in the modern age,
due to historic reasons, almost all countries use :

(a) the Gregorian calendar for regulation of
civic and administrative life,

(b) their own characteristic calendars for regu-
lation of social and religious observances.

0. B. — 80

172

BEPORT OF THE CALENDAR REFORM COMMITTEE

For example, India uses the Gregorian calendar for
civic and administrative purposes, but various, luni-solar
calendars for fixing up dates for religious festivals of
Hindus in different states. The Islamic countries also
follow the same practice — Gregorian calendar for civic
and administrative purposes, but the lunar calendar
for religious purposes.

Even in Christian countries, which apparently use
the Gregorian calendar for both purposes, in actual
practice, some additional time-reckonings have to be
done for fixing the date of Easter and other holi-
days which move with it. These reckonings constitute
the ecclesiastic calendar, and are survival of earlier
luni-solar calendars.

The disadvantages of the Gregorian calendar as
used for, civic and administrative purposes are :

(a) that the years and months begin on different
week days,

(b) that months are of unequal length—from 28
to 31 days — and they start on week-days
which are most changeable.

This happens because a normal year of 365 days
consists of 52 weeks plus one day ; and a leap-year
coming every fourth year, has 366 days, and consists of
52 weeks plus 2 days. If a normal year begins on a
Sunday, the next year will start on Monday, and the
year after a leap-year will jump two week-days.

This causes a most undesirable wandering of the
^week-day on which the year begins, as is seen for the
Tiext few years. This year 1954, has started on a
Friday. We shall have

1955 starting on Saturday

1956 „ „ Sunday

1957 „ „ Tuesday

1958 „ „ Wednesday

1959 „ „ Thursday

1960 „ „ Friday

1961 „ „ Sunday

How much better it would be for civic and adminis-
trative life if a system could be devised that every year
should start on a Sunday ?

The World Calendar Plan

This is how the World Calendar Plan proposes to
prevent this wandering of the starting-day of the * year.
It is a very simple device.

If from 1961, which starts on a Sunday, the last day
of the year (ix. Dec. £1) which would be under the
present system a Sunday, is called the Worldsday, that
is, no week-day denomination is attached to it, then
1962 also will start on a Sunday, and so will every year
till the next leap-year 1964. On that year another

additional day, the Leap- Year Bay, is inserted at the
end of June, and have the usual Worldsday at the end
of the year ; then 1965 will also start on a Sunday.

So, by this simple device of having a Worlds-day
at the end of every year and a Leap-Year Day at the
end of June every fourth year, both without any
week-day denomination, every year can be made to
start on a Sunday, This will prove to be an inestimable
advantage for the civic life of mankind.

It is needless to add illustrations of the chaotic way
in which the starting week-days of months vary. They
are chaotic, because lengths of months vary from 28
to 31. There is not the slightest scientific justifica-
tion for these varying lengths. They are said to have
been due to the caprice of two Roman dictators, or
some other historical cause not yet clear. How much
better it would be for civic purposes, if each month
could start on a fixed day of the week ?

The World Calendar plan proposes to put this right
by dividing the year into four quarters, each of three
months of 31, 30, 30 days' duration. According to this
plan,

January, April, July, October would have each
31 days, and start on Sunday,

February, May, August, November would have each
30 days, and start on Wednesday,

March, June, September, December would have
each 30 days, and start on Friday.

If this plan be adopted, the calendar will be perpe-
tual and fool-proof. What a welcome change it would
prove when compared to the present chaotic and
wandering calendar ?

The year has to conform to the period of the sun,
and this is covered by the leap-year rules, amended
by Pope Gregory XIII in 1582. The leap-year rules
introduced by the Iranian poet-astronomer Omar
Khayyam in 1079, were more accurate, but less
convenient. The Gregorian leap-year rules will
cause a mistake of only one day in 3,300 years, which
is trivial.

As regards the duration of months, the World
Calendar plan is a marked improvement on the
chaotic lengths and starting days of months, inherited
from the Julian calendar, which has been tolerated
too long. The months of all the quarters are identical
and have got 31, 30 & 30 days, commencing on
Sundays, Wednesdays and Fridays respectively. Each
month has thus got exactly 26 working days. It has
retained the present 12 months, thus the four quarters
are always equal, each quarter has 3 months or 13
weeks or 91 days beginning on Sunday and ending
with Saturday.

THE SOLAB CALENDAR

173

The objections to the World Calendar plan come
from several Jewish organizations, on the ground that
the World Calendar plan interferes with the
unbroken seven-day week, by introducing Worlds-
day and Leap-year - Day without any week-day
denomination. This, they say, will interfere with
their religious life.

As already shown, the religious sanction for the
seven-day cycle is either non-existent, or slight,
amongst communities other than the Jews, and even
amongst them, it dates only from the first century A. D.
The claims of certain Jewish Rabbis to prove that the
seven-day week cycle has been ordained by God
Almighty from the moment of creation which event,
according to these Jewish Rabbis, took place on the
day of the autumnal equinox, also a new moon day,
is a fantastic conception of medieval scholars, which
no sane man can entertain in these days of Darwin and
Einstein.

The World Calendar plan has no intention of
interfering with, the characteristic calendars of
communities or nations. They can exist side by side
with the World Calendar. For such communities as
intend to maintain the continuous seven-day week,
their religious week-days, including Sundays, would
no doubt wander through the World Calendar week-
days, and cause some inconvenience to the very small

fraction of people who would want to observe their
religious rites accprding to established usage.

But these inconveniences can be adjusted by
agreement, and it would be egoistical on the part of
a particular community or communities to try to
impede the passage of a measure of such great useful-
ness to the whole of mankind on the plea that the
World Calendar plan interferes with the continuous
seven-day week. Calendars are based on Science,
which everybody must bow to ; and on Convention,
which may be altered by mutual consent. The
unbroken seven-day week is a Convention^ but the
World Calendar plan has proposed a far better Conven-
tion, which should be examined on its own merits.*

As a result of a request from the Government of
India, the proposal of the World Calendar Reform
had become the subject of discussion at the eighteenth
session of the Economic and Social Council of the
United Nations held at Geneva during June- July,
1954. Professor M. N. Saha, F. R. S., Chairman,
Calendar Reform Committee, attended the ECOSOC
meeting at Geneva to explain the desirability of the
proposed reform.

* Being the full text of the address in support of the Indian
proposal for World Calendar reform, by Prof. M. N. Saha, F.R.S- at
the 18th Session of the Economic and Social Council of the United
Nations, held at Geneva in June-July, 1954.

THE WORLD CALENDAR

JANUARY

S M T W T F S

1 2 3 4 5 6 7
8 9 10 11 12 13 14
15 16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31

FEBRUARY

S M T W T F S

12 3 4
5 6 7 8 9 10 11
12 13 14 15 16 17 18
19 20 21 22 23 24 25
26 27 28 29 30

MARCH

S M T W T F S

1 2

3 4 5 6 7 8 9
10 11 12 13 14 15 16
17 18 19 20 21 22 23
24 25 26 27 28 29 30

APRIL

S M T W T F

12 3 4 5 6 7
8 9 10 11 12 13 14
15 16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31

MAY

S M T

T F S

12 3 4
5 6 7 8 9 10 11
12 13 14 15 16 17 18
19 20 21 22 23 24 25
26 27 28 29 30

JUNE

M T W T F S

1 2

3 4 5 6 7 8 9
10 11 12 13 14 15 16
17 18 19 20 21 22 23 L,
24 25 16 27 28 29 30 W|

JULY

S M T W T F S

1 2 3 4 5 6 7
8 9 10 11 12 13 14
15 16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31

AUGUST

S M T W T F

12 3 4
5 6 7 8 9 10 11
12 13 14 15 16 17 18
19 20 21 22 23 24 25
26 27 28 29 30

SEPTEMBER

s m T w t f s

1 2

3 4 5 6 7 8 9
10 11 12 13 14 15 16
17 18 19 20 21 22 23
24 25 26 27 28 29 30

OCTOBER

S M T W T F S

1 2 3 4 5 6 7
8 9 10 11 12 13 14
15 16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31

NOVEMBER

S M T W T F S

12 3 4
5 6 7 8 9 10 11
12 13 14 15 16 17 18
19 20 21 22 23 24 25
26 27 28 29 30

DECEMBER

S M T W T F S

1 2

3 4 5 6 7 8 9
10 11 12 13 14 15 16
17 18 19 20 21 22 23L-
24 25 26 27 28 29 30 W|

W <Worldiday, a World Holiday) ttttb 31 DtetuWr (365th day) and fottowi 30 Dtcim-

ber mry yu». _
W (Lupytar Day. another World Holiday) «Q<»U 31 Jtmt and follow* 30 Jwo in too ytars.

In this Improved Calendar :

Every year is the same.

The quarters are equal : each quarter has
exactly 91 days, 13 weeks or 3 months ; the
four quarters are identical in form.

Each month has 26 weekdays, plus Sundays.

Each year begins on Sunday, 1 January ; each
working year begins on Monday, 2 January.

Each quarter begins on Sunday,, ends on
Saturday.

The calendar is .stabilized and perpetual, by
ending the year with a 365th day that follows
30 December each year, called Worldsday dated
"W" or 31 December, a year-end world holiday.
Leap-year day is similarly added, at the end of
the second quarter, called Leapyear Day dated
"W" or 31 June, another world holiday in
leap years.

CHAPTER III

The Luni-Solar and Lunar Calendars

3.1 PRINCIPLES OF LUNI-SOLAR CALENDARS

The Egyptians appear to have been the only
cultural nation of antiquity who discarded the moon
entirely as a time-marker. Other contemporaneous
cultural nations, e.g., the Sumero-Akkadians of
Babylon, and the Vedic Indians retained both the sun
and the moon as time-markers, the sun for the year, the
moon for the month.

The Indian astronomers called the moon masakrt,
(month-maker) and before the Siddhanta Jyotw time,
the moon was considered more important as a time-
marker than the sun (tide §5). It was the same with
other nations too, for as Pannekoek remarks, we find
the opinion written in the sacred books of many
nations "For regulating time, the moon has been
created'*.

The retention of both the sun and the moon,
however, gives rise to a multitude of problems, of which
a fair summary is given by Pannekoek as follows.*

"With all peoples of antiquity, the Indians, Babylonians,
Jews, Greeks, we find the moon-calendar used ; the period
of the moon, the regular sequence of the first appearance of
the fine crescent moon in the evening sky, its growth to first
quarter, to full moon, at the same time coming up later and
filling the whole night, then the decrease to last quarter till
its disappearance after the last thin crescent before sunrise
was seen,— this regular cycle of the moon's phases in the
period of 29i days was everywhere the first basis of
chronology".

"But the calendar could not be satisfactorily fixed with
the establishment of the moon-cycle. In these ancient
times, the people, the tribe, and the state was » political,
spiritual and religious unity. Important events of society,
the great agricultural performances, the beginning of the
ploughing, the sowing or the harvesting were great popular
festivals and at the same time chief religious ceremonies,
when offerings were presented to the gods. The moon
calendar had to adapt itself to the economic life of the
people, which was governed by the cycle of seasons. Thus
arose the practical problem of adapting the moon-period of
29i days to the solar year of 365 days. Thin chief problem
.of ancient chronology has been a mighty impulse to the study
of astronomy, because it necessitated continuous observation
of the sky"

'~*~~i^r^'jis^ioSV <™d its influence upon the development
of Astronomy' by Anton Pannekoek, published in the Journal of the
Royal Astronomical Society of Canada, April, 1930.

Twelve lunar months of 29£ days each, making a
total of 354 days, fall nearly 11 days short of the solar
year. In the next year, the beginning of each month
occurs 11 days earlier, in three years 33 days will be
lost.* To fix the same month to the same season
always, there are no other means than after two or
three years to intercalate a Thirteenth Month, number
13, by repeating the last month of the year.

The luni-solar adjustment which is next taken up
is the first step to the solution of problems stated by
Pannekoek, but it is not however the whole solution,
for it leaves untouched the problem of correct predic-
tion of the day when the crescent of the moon first

appears after new moon in the western horizon. This

will be taken up later (vide §4).

Luni-solar adjustment can be satisfactorily made

if we have accurate knowledge of the length of the

tropical year, and of the mean length of the lunation.

Let us see how these fundamental periods were

determined in ancient times.

Length ot Seasons and the Year

The length of the year was obtained in Egypt, as
we have already seen, from the recurrence of the Nile
flood. In Babylonia, no such striking natural
phenomena were available. It is very probable that
the Babylonians early learnt the use of the gnomon,
with the aid of which they could determine the
cardinal days of the year : <oix. y the summer and winter
solstices, and the two equinoxes coming in between.

The lengths of the seasons were found by counting
the number of days from one cardinal day to the next.
The number may vary' by one day from year to year,
and astronomers must have realized that the correct
length of a season was not a whole number but was
fractional. Probably the correct length was found by
taking a large number of observations, and taking the
mean. The following table shows the length of the
seasons and of the year as found by ancient
astronomers.

* The mean duration of ft lunar month consists of 29*530688
days and twelve such lunations amount to 354*36706 days, while the
length of a tropical solar year is 365*4220 days. The length of a
lunar year thus falls short of the solar year hy 10.87514 days, and
instead of there being exactly twelve lunar months in ft year, there
are 12.36827 months.

174

THE LUNI-SOLAE AND LUNAR CALENDARS

175

Table 2. — Showing the length of seasons.

Euctemon Calippos Chaldean Correct

values for

(432 B.C.) (370 B.C.) (200 B.C.) 1384 B.C.

days

Spring

94.50

94.09

Summer

9273

91*29

Autumn

88*59

88.58

Winter

89'44

91'29

Total —

365

365.26

365.25

The length of the year was also found by the same
method. The solar year is the period between
successive transitions of the sun through the same
cardinal point, Neugebauer thinks that summer
solstice was first used for this purpose in ancient
times. But subsequently evidences are found of the
use of other cardinal points.

Thus we find that during the classical period in
Babylon, the solar year started with the vernal
equinox. But the Macedonian Greeks and the Jews
started with the autumnal equinox. The west
European countries appear to have started the solar
year with the winter solstice.

The number of days in a solar year would vary
between 365 and 366. Probably the exact length was
determined by counting the number of days between the
year-beginnings separated by a large number of years
and taking the mean. The Indian practice, followed in
the Siddhantas, is to give the number of days in a
Kalpa (a period of 4.32x10° years) from which one
can find out the number of days in a year by simple
division. This appears in modern times to be a rather
cumbrous practice, but is probably reminiscent of
taking the mean for a large number of years.

In ancient times, people had not learnt to follow
the motion of the sun in the starry heavens, so they
were unaware of the difference between the ( sidereal
year and the tropical year. But from their method of
measurement, they unconsciously chose the correct, or
the tropical year.

Modern measurements show that the length of the
tropical year is not constant, but is slowly varying.
It is becoming shorter at the rate of "0001 days or 8*6
sees, in 1600 years.

So that in Sumerian times, the tropical year had
a length of 365.2425 days. The present length is
365-2422 days.

3.2 MOON'S SYNODIC PERIOD OR LUNATION :
EMPIRICAL RELATION BETWEEN THE YEAR
AND THE MONTH

The solar year has thus a pretty nearly constant
value, but even the earliest astronomers appear to
have observed, that the lunation, or the synodic period
of the moon is not a constant, but is variable. As a
matter of fact, the period varies from 29*246 to 29.817
days— nearly fourteen hours. The observation of the
actual motion of the moon formed the most formidable
problem in ancient astronomy {vide §4).

But all ancient nations show knowledge of an
astonishingly correct value of the mean synodic period,
which is known to be 29.530588 days. This is probably
because they could count the number of days with
fractions comprising a very large number of lunations,
and therefore the mean value came out to be very
correct.

With the aid of the knowledge of correct values of
the length of the tropical year, and of the mean
synodic period of the moon, it is possible to find out
correct rules for luni-solar adjustment, as narrated
below. But this could happen only at a later stage.
The first stage was certainly empirical as is clearly
indicated from a record of the great Babylonian king
and law-giver Hammurabi (1800 B. C), which says that
the thirteenth month was proclaimed by royal order
throughout the empire on the advice of priests. All
religious observances were forbidden during this
period.*

It is not known however, what principles, if any,
guided the king or rather his advisers in their selection
of the thirteenth month, but most probably the
adjustment was empirical, i.e., the month was discarded
wlien the priests found 'from actual experience that
the festival was going out of season. Many ancient
nations who used the luni-solar calendar, do not
appear to have gone beyond the empirical stage.

Empirical Relations between the Solar and Lunar
Periods : The Intercalary Months.

The Chaldean astronomers (as the Babylonians
were called after 600 B.C.) appear to have striven
incessantly to obtain very accurate values for the
mean lunation and the length of the solar . year, and

* It is said that in ancient Palestine, the custom was that the
Rabbis went to tjie fields and watched the time by their calendar for
the ripening of wheat. * If the lunar month of Addaru (last month of
the year) fell back too much towards winter, they would proclaim a
second Addaru in that year, so that the first of Nisan would coincide
roughly with the ripening of wheat

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work oat at the discovery of mathematical relation-
ships between these two periods having the form-

m lunar months =w solar years
where both <m and n are integers.

Let us describe some of these relations.
The Octaeteris : This depends on the relation :

8 tropical years ==2921 .94 days
99 lunar months =2923.53 days.

The difference is only 159 days in 8 years. We
have used here the correct lengths of the two periods.
The Babylonian values were slightly different.

According to this relation, there were to be three
extra or intercalary months in a period of 8 years, and
festivals would fall approximately in the right seasons,
if these three months were suitably excluded for
religious observances. But the rule was only approxi-
mate. In a few cycles, the discrepancy would be too
large to be disregarded.

According to the celebrated exponent of Baby-
lonian astronomy, Father Kugler, this system was in
vogue from 528 B.C. to 505 B.C., then there was an
interval when they used to have 10 intercalary months
in a period of 27 years. From 383 B.C., the Chaldeans
used the 19-year cycle, based on the relation :

19 solar years -6939.60 days
235 lunar months =6939.69 days.

There is a discrepancy of .09 days in 19 years, or a
mistake of 1 day in 210 years.

The 19-year cycle, with 7 intercalary months was
used throughout the whole Seleucid times (313 B.C.-
75 B.C.), as shown by Pannekoek. This system has
not been superseded inspite of various attempts.

These rules came into vogue at a time (383 B.C.),
when Babylon had lost her independence and became
a vassal state of the Persian empire of the Achemmids.
We do not know what was the original calendar of
pre-Acheminid Persia, but the great Acheminid
emperor Darius preferred the simpler Egyptian solar
calendar to the complex luni-solar calendar of Babylon.
The population of Babylon could no longer depend
upon the king to adjust the dates of their religious
observances by royal decree, as happened in the time
of Hammurabi (1800 B.C.). Probably therefore the
priest-astronomers felt the need of mathematical rules
which should take the place of royal decrees.

Table 3.— The 19-year cycle.

Cycle of 19 years showing Intercalary Months

(Compiled from Pannekoek' 9 calculation of dates
in Babylonian Tables of planets)

Year in the
19-year cycle

2
3

9*
10
11
12*
13
14
15*
16
17

18+
19

Total no. of
days
384
354
355
384
355
354
384
354
384

355

354

384

355

354

384

354

355

383

354

Tears of the
Seleucidean Era

134 153 172

135 154 173

136 155 174

137 156 175

138 157 176

139 158 177

140 159 178

141 160 179

142 161 180

143 162 181

144 163 182

145 164 183

146 165 184

147 166 185

148 167 186

149 168 187

150 169 188

151 170 189

152 171 190

191 210 229

192 211 230

193 212 231

194 213 232

195 214 233

196 215 234

197 216 235

198 217 236

199 218 237

200 219 238

201 220 239

202 221 240

203 222 241

204 223 242

205 224 243

206 225 244

207 226 245
2C8 227 246
209 228 247

Total

6940

N. B. Years marked * have a second Addaru,
and years marked + have a second Ululu.

312- Seleucidean era«Christian era B.C.

(Jan. to Sept.)

Seleucidean era -311 -Christian era A.D.

(Jan. to Sept.)

The 'Nineteen-year cycle* is generally known as
the 'Metonic Cycle' after Meton, an Athenian
astronomer who unsuccessfully tried to introduce it
at Athens in 432 B.C. But there is no proof that it
was used at Athens before 343 B.C. The question of
'priority' of this discovery is therefore a disputed one.

3.3 THE LUNI-SOLAR CALENDARS OF THE BABY-
LONIANS, THE MACEDONIANS, THE ROMANS,
AND THE JEWS

In addition to the Chaldeans, many other nations
of antiquity, viz., the Vedic Indians, the Greeks, the
Romans and the Jews and others used the luni-solar
calendar, and had to make luni-solar adjustments.
It will be tedious to relate how they did it, except
in the case of the Vedic Indians (vide § 5). But the
knowledge of the nineteen-year rule appears to have
diffused to all countries by the first century of the
Christian era. From this time onwards, the lunar
months of different nations appear to be interchange-
able. This is shown in the following Table No. 4.

We have almost complete knowledge of the luni-
solar calendars or the Babylonians during Seleucid
times. The names of months with their normal lengths
are shown in column (2) of the table.

THE LUNI-SOLAK AND LUNAK CALENDARS

177

Table 4. — Corresponding Lunar months.
Lunar Month-Names

(1)

(2)

(3)

(4)

Indian

Chaldean

Macedonian

Jewish

CAITRA

Addaru

Xanthicos

Vai&akha

NISANNU (30) Artemesios

Nissan

Jyai§£ha

Aim

(29) Daisios

Iyyar

A§adha

Sivannu

(30) Pancmps

Sivan

Sravana

Duzu

(29) Loios

Tararauz

Bhadra

Abu

(30) Gorpiaios

Asvina

Ululu

(29) Hyperberetrios

Ellui

Kartika

Tasritu

(30) DIOS

TISHRI

Margaslrsa Arah

Samnah

(29) Appclaios

Marheshvan

Pausa

Kisilibu

(30) Audynaios

Kislev

Magha

Dhabitu

(29) Peritios

Tebeth

Phalguna

Shabat

(30) Dystros

Shebat

Caitra

Addaru

(29) Xanthicos

Adar and
Veadar

The first Babylonian month Nisannu, started with
30 days, and other months were alternately 29 and 30
days. A normal year thus consisted of 354 days, but
occasionally an extra day was added to the last month,
and it became a year of 355 days.

The effect of these intercalations was that the first
month, viz., the month of Nisannu, never strayed for
more than 30 days beyond the day of vernal equinox.

As the table shows, the Babylonian year might be
of 354, 355, 383, or 384 days duration, and occasio-
nally it is said that they extended to 385 days. It
was therefore impossible to calculate the number of
days between two incidents, dated accoiding to the
Chaldean calendar, unless the investigator had a table
of past years showing the lengths of each individual
year. Herein comes the superiority of the Egyptian
system, where the number of days between two
incidents, dated according to the Egyptian system,
could be easily calculated. The two greatest astro-
nomers of ancient times, Hipparchos and Ptolemy,
therefore, preferred the Egyptian system of dating to
the Chaldean or the Macedonian.

The Macedonian Greeks used the months given
in column (3) in their home land. When they settled
in Babylon as rulers (313 B.C.), they continued to use
the same months, but got them linked to Chaldean
months. Their first month was Dios, which was
the seventh month of Chaldeans. This was probably
linked to the autumnal equinox in the same way as
Nisannu was to the vernal equinox. The Macedonian
year started six months earlier than the Chaldean year.

The Macedonian months were used by the
Parthians, the early Sakas, and the Kushans in India
wihout change of name (vide § 5-5), and probably the

month-lengths were also the same as in the Chaldean
19-year system. When the Sakas and Kushans began
to rule in India, from first century B.C., they used
the Macedonian months alternatively with the Indian
months which are shown in the first column. The first
Indian season, Spring, however according to imme-
morial Indian custom, has been on both sides of the
vernal equinox ( — 30° to 30°), while in the Graeco-
Chaldean system, the Spring started with vernal
equinox (0°). The first Indian month is Caitra, the
first of the spring months, and according to rules
prevalent in Siddhantic times (300 A.D.), the month
was to be always on the lower side of the vernal
equinox, i.e., the beginning of lunar Caitra was to be on
a date before the vernal equinox. It may be added that
the Indian lunar months mentioned here are amanta
or new moon ending.

3.4 THE INTRODUCTION OF THE ERA

For accurate date-recording, we require besides
the month and the day, also a continuously running
era. But the era came rather late in human history.
We find dated records of kings in Babylon from about
1700 B.C. (Kassite kings). They used regnal years,
lunar months, and the day of the lunar month. The
ancient Egyptian records do not use any era, but
sometimes the regnal years. But the use of regnal
years is very inconvenient for purposes of exact
chronology, because one has to locate the beginning
of the reign of the king on the time-scale which often
proves to be an extremely difficult problem, e.<?., in
India, Emperor Asoke used regnal years, but it is a
problem of nearly hundred years for archaeologists
to find out the exact date of the commencement of
his reign. This varies from 273 B.C. to 264 B.C.

In the writings of the Greek astronomers Hippar-
chos (140 B.C.) and Ptolemy (150 A.D.), we come across
an era purporting to date from the time of one king
Nabu Nazir of Babylon (747 B.C.), who is known to
history, though this era is not used in records of the
Babylonian kings themselves.

The inference has been made, though without
clear proof, that the Babylonian or rather Chaldean
astronomers who were the earliest systematic observers
of the heavenly bodies, get tired of the use of the
regnal years, and felt the need of a continuously
running era for precision in time-reckoning. They
took advantage of a unique gathering of planets about
Feb. 26, 747 B.C. when Nabu Nazir was reigning in
Babylon to proclaim that the gods have ordained the
'introduction of a continuously running era' ( Shy and
Telescope, Vol. I, p. 9, April, 1942).

But the use of the Nabonassar era appears to have
been confined to astronomers. The kings continued

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REPORT OF THE CALENDAR REFORM COMMITTEE

to record events, in their regnal years as this had
a great propaganda value for the royal family which
they were unwilling to forego.

It is now known that the other ancient eras, like
that of the Greek Olympiads (776 B.C.) or the era of
Foundation of Rome (753 B.C.) are extrapolated eras.
The ancient Greek method of dating by Olympiads is
of uncertain origin, but the system was critically
examined by the Alexandrian chronologists, parti-
cularly Eratosthenes (3rd century B.C.), the founder of
scientific chronology. According to the Encyclopaedia
Britannica, 14th edition, Greek chronology is not
reliable till the 50th Olympiad (i.e. 576 B.C.). The
era was therefore invented a long time after its alleged
year of starting. The era of the Foundation of Rome
had a similar history (see Encyclopaedia Britannic* 14th
edition, Chronology). The starting years of these eras
are suspiciously close to that of the Nabonassar era
(747 B.C.). Probably both these eras were plagiarized
from the era of Nabonassar after the savants of
ancient Greece and Rome acquired the time-sense.

It is noteworthy that Hipparchos and Ptolemy used
neither the era of Olympiads nor the era of Foundation
of Rome, nor Greek or Chaldean months which were
lunar, but the Nabonassar era and the more con-
venient Egyptian solar months. They preferred
science to nationalistic chauvinism.

The Seleucidean and other derived Eras

The Seleucidean Era (the S. E. era) : The first
continuously running era which ran into general
circulation is that introduced to commemorate the
foundation of Seleucus's dynasty and dates from the
year when Seleucus occupied the city of .Babylon
after defeating his rivals. There were two methods
of counting, differing in the initial year and the first
day of the year.

According to the official (Macedonian) reckoning,
the era started from the lunar month of Dios (near
autumnal equinox) in the year (—311) A.D. or 312 B.C.
The months had Macedonian names.

According to the native Babylonian reckoning, the
era started from the lunar month of Nisan (near
vernal equinox) six months later than the starting of
the Macedonian year. The months had Chaldean
names, as given in Table No. 4.

The Seleucid monarchs ruled over a vast empire
from Syria to the borders of Afghanistan from 311 B.C.
to 65 B.C. i.e., nearly for 250 years and under their
rule, the knowledge of Graeco-Chaldean astronomy
and time-calculations spread far and wide, ultimately
reaching India, and profoundly modifying the indige-
nous system in India. The use of Macedonian months

spread over all these countries, as is apparent from
contemporary inscriptions and coin-datings mentioned
in § 5*5. The months were amanta, i.e., started after
the new-moon was completed and were pegged on to
the solar year which started on the day of the vernal
equinox. The Nisan was the first lunar month after
the vernal equinox. There were 7 intercalary months
in a period of 19 years. The correspondence between
Chaldean and Greek months and the position of the
intercalary months have been worked out by Prof.
Pannekoek between the years 134-247 of the Seleuci-
dean era, as already given (vide § 3-2 and 3-3) along
with their Indian equivalent lunar months.

The Parthian Era

Since the introduction of the Seleucidean era, the
practice arose for a nation or a dynasty to start eras
commemorating some great event in their national or
dynastic life. The first in record is the Parthian era,
and the story of its starting is well-known. The
Seleucid emperors ruled the Near East from 312 B.C.
imposing on the countries under their domination
Greek culture, the Seleucidean era, and the Graeco-
Chaldean system of time-reckoning. About 250 B.C.,
there were wide-spread revolts against Seleucid rule in
Bactria, in Parthia (Eastern Persia), and other parts
of the Near East. The revolt in Parthia was led by
one Arsaces and his brother Tiridates who belonged
to an Iranian tribe, which had adopted Greek culture.
To commemorate their liberation from Seleucidean
rule, the Parthians introduced an era, beginning
64 years after the Seleucid era (i.e. 248 B.C.). But
at first this era (Arsacid era) was only rarely used.
The early Parthian emperors preferred to use on
their coins the Seleucidean era, the Macedonian
months, and the Graeco-Chaldean system of time-
reckoning inscribed in Greek letters. In the first
century A.D., there was a Zoroastrian revival, the
S.E. was dropped in favour of the Parthian era and
Pehlevi began to be used in place of Greek, though
Macedonian month-names were still kept.

Though kings bearing Parthian names ruled at
Taxila about the first century B.C. to first century A.D.,
e.g., king Gondophernes, no clear evidence of the
use of the Parthian era on Indian soil has yet
been found.

It is very likely that the Saka era, with its methods
of calendar-reckoning, which came into vogue in
India during the Siddhctnta Jyotisa times, was started
by the Saka tribes when they attained prominence,
and started an era of their own, in imitation of the
Parthians. They, however, retained the Graeco-
Chaldean method of lunar month-reckoning and
probably the same system of intercalary months.

THE ljUNT-SOLAK A&D LtTNAK CALENDARS

179

3.5 THE JEWISH CALENDAR

The ancient Jewish calendar was lunar, the
beginning of the month being determined by the first
visibility of the lunar crescent. As the month-names
show (col. 4 of the table No. 4 ), they were evidently
derived from the Babylonian month-names excepting
one or two, viz., Marheshvan and Tammuz. The day
began in the evening and probably at sunset. The year
used to begin with the spring month Abib or Nisan,
the latter being the Babylonian name of the month
which was adopted by the Jews in the post-exilic
times. Intercalation was performed, when necessary,
repeating the twelfth month f Adar which was then
known as 'Veadar' followed by Adar. The year-
beginning was subsequently changed and in the last
century before Christ, it became the month of Tishri,
corresponding to the Macedonian month of Bios. This
must have been due to the desire or need to follow
the practice of the ruling race.

Originally there were no definite rules for inter-
calation and for fixing up the beginning of the months.
Because various religious festivals and sacrifices were
fixed with reference to the beginning of the month,
information about it was spread throughout the
country by messengers and by signal fires on hilltops.

About the 4th century A.D., fixed rules were
introduced in the calendar and nothing was left to
observation or discretion. Intercalation is governed
by a 19-year cycle in which the 3rd, 6th, 8th f 11th,
14th, 17th and 19th years have got an extra month.
The actual beginning of the initial month of the year,
vix., Tishri is obtained from the mea'n new-moon by
complicated rules which are designed to prevent
certain solemn days from falling on inconvenient
days of the week. As a result, a common year may
consist of 353, 354 or 355 days and an embolismic or
leap-year of 383, 38*4 or 385 days. Ten of the months
have got fixed durations of 29 or 30 days, as well as
the intercalary month which contains 30 days, the
other two varying according to the requisite length
of the year.

The Jewish Era of Creation

The Jews use an Era {Anno Mun&i, libriath olum)
or 'Era of Creation which is supposed to have been
started from the day of creation of the world. We
quote the following passages from Encyclopaedia
Britanmca; 14th edition, 'Chronology, Jewish'.

(l) The era is supposed to begin, according to the
mnemonic Beharad, at the beginning of the lunar cycle on
the night between Sunday and Monday, Oct. 7, 3761 B.C.,
at 11 hours Hi minutes P.M. This is indicated by be (beth,

two, i.e., 2nd day of week), ha (he, five, i.e., fifth hour after
sunset) and Bad (Besh, dalet, 204 minims after the hour).

(2) In the Bible various eras occur, e.g., the Mood, the
Exodus, the Earthquake in the days of King Uzziah, the
regnal years of monarchs and the Babylonian exile. During
the exile and after, Jews reckoned by the years of the
Persian kings. Such reckonings occur not only in the Bible
(e.g., Daniel viii, I) but also in the Assouan papyri. After
Alexander, the Jews employed the Seleucid era (called
Minyan Shetaroth, or era of deeds, since -legal deeds were
dated by this era). So great was the influence exerted by
Alexander, that this era persisted in the East till the 16th
century, and is still not extinct in south Arabia. This is the
only era of antiquity that has survived. Others, which fell
into disuse, were the Maccabaean eras, dating from the
accession of each prince, and the national era (143-142 B.C.),
when Judaea became free under Simon. That the era
described in Jubilees was other than hypothetical, is
probable. Dates have also been reckoned from the fall of
the* second Temple [Le-Horban hab-bayyith). The equation
of the eras is as follows.:

Year 1 after destruction = A.M. 3831

= 383 Seleucid
= A.D. 71

The 'Era of Creation* is supposed to have started
from the day of autumnal equinox of the year 3761 B.C.
So the sun and the moon must have existed before the
day of creation !!

3.6 THE ISLAMIC CALENDAR

The Mohammedan calendar is purely lunar and
has no connection with the solar year. The year
consists of 12 lunar months, the beginning of each
month being determined by the firtt observation of the
crescent moon in the evening sky. The months have
accordingly got 29 or 30 days and the year 554 or 355
days. The new-year day of the Mohammedan calendar
thus retrogrades through the seasons and completes
the cycle in a period of about 32-J solar years.

The era of the Mohammedan calendar, viz., the
Hejira (A.H.), which was probably introduced by the
Caliph Umar about 638-639 A.D., started from the
evening of 622 A.D., July 15, Thursday*, when the
crescent moon of the first month Muharram of
the Mohammedan calendar was first visible. This
was the new-year day preceding the emigration
of Muhammad from Mecca which took place about
Sept. 20 (8 Rabi I), 622 A D.

*As the. day of the Islamic calendar commences from 4unset r
Friday started from the evening of that day.

C. B.-31

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REPORT OF THE CALENDAR REFORM COMMITTEE

For astronomical and chronological purposes the
lengths of the months are however fixed by rule and
not by observation. The lengths of the months in days
for this purpose are as follows :

rviunariaiii

...30

udldl

Rabi-ul awwal

Rabi-us sani

Jamada'L awwal

Jamada-s sani

Rajab

Shaban

Ramadan

Shawal

Zilkada

Zilhijja

29 (or 30)

The leap-year, in which Zilhijja has one day more,
contains 355 days and is known as Kabishah, In a cycle
of 30 years, there are 19 common years of 354 days and
11 leap-years of 355 days. Thus 360 lunations are made
equivalent to 10,631 days or only '012 days less than
its actual duration. The rule for determining the leap-
year of this fixed calendar is that, if after dividing the
Hejira year by 30, the remainder is 2, 5, 7, 10, 13, 16,
18, 21, 24, 26 or 29, then it is a leap-year.

The only purely lunar calendar is the 'Islamic
calendar', which has been in vogue amongst the
followers of Islam since the death of the Prophet
Muhammad (632 A.D.). But it is well-known that
before this period Mecca observed some kind of luni-
solar calendar in common with all countries of the
Near East. The common story is that when pilgrims
from distant countries and other parts of Arabia came
to perform Hajj at Mecca (Hajj is a pre-Islamic
practice), they often found that it was an intercalary
month according to Meccan calculation, when no
religious festival could be performed, and had to wait
for a month before they were allowed to perform the
rites. This meant great hardships for distant visitors
and to prevent recurrence of such incidents the
Prophet forbad^ the use of intercalary or 13th month
and decreed that the calendar should henceforth be
purely lunar.

It has now been shown by Dr. Hashim Amir Ali of
the Osmania University, Hyderabad, that the Moha-
mmedan calendar was originally luni-solar in which
intercalation was made when necessary, and not
purely lunar. This view-point has now been strongly
supported by Mohammed Ajmal Khan of the Ministry
of Education, Govt, of India. They emphasize that
upto the last year of the life of Mohammed, i.e., upto
A.H. 10 or A.D. 632, a thirteenth month was inter-
calated when necessary. The Arabs, among whom
there were relatively few men conversant with astro-
nomical calculations^ had a system in which a family
of astronomers, known as Qalammas was responsible
for proclaiming at the Hajj (falling in the last month
of the year : Zilhijja) that a thirteenth month would or
would not be added. Astronomically such intercala-
tion should be made 3 times in 8 years or 7 times in 19
years. The elder of the Qalamma had a certain amount
of discretion in determining when this intercalation
was to be practised, and this very practice afterwards
caused great confusion.

According to this view, proper intercalation was
applied in all the years where necessary upto A.H. 10
and consequently the year A.H. 11 (coming next, to
the Hajj of A.H. 10) which started on March 29, 632
A.D. {i.e., after the vernal equinox day) seems to have
been a rather normal year, and as such all the previous
new-year days appear to have been celebrated on the
visibility of the crescent moon after the vernal equinox
day. The Muslim months should accordingly occupy
permanent places in the seasons as follows* ; —

Muharram... Mar. — April Rajab ...Sept— Oct-

Safar April— May Shaban ...Oct.— Nov.

Rabi I ... May — June Ramadan . . Nov. — Dec.

Rabi II ... June —July Shawal ...Dec. — Jan.

Jamadi I ... July —Aug. Zilkada . . Jan. —Feb.

Jamadi II ... Aug.— Sept. Zilhijja ...Feb. —Mar.

~^Mi this view is accepted, it would then be necessary to shift the
starting epoch of the Hejira era, which is commonly accepted as July
16, 622 A.D., to an earlier date, as 4 intercalary months or 118 days
will then have to be inserted between the new-year days of A.H. 1 and
of A.H. 11, which is March 29, 632 A.D. The initial epoch of the
Hejira era thus arrived at is the evening of March 19, 622 A.D.,
Friday, the day following the vernal equinox.

CHAPTER IV

Calendaric Astronomy

4.1 THE MOON'S MOVEMENT IN THE SKY

The scheme of lunar months given in Table No* 4
in a nineteen-year period, which came into vogue in
Babylon about 383 B.C. did not however, completely
satisfy the needs of the Babylonian calendar, because
for religious purposes, the month was to start on the
day the crescent moon was first visible in the western
horizon after conjunction with the sun (the new-

and the moon move uniformly in the same great
circle in the heavens. But even the, most primitive
observers could not fail to notice that neither do the
two luminaries move in the same path, nor do they
move uniformly, each in its own path.

The motion of the moon amongst the stars is the
easiest to observe. This is illustrated in the two
figures reproduced from the Sky and Telescope, giving

Fig. 2— Showing the positions of the sun, moon and planets among the stars in June. 1953,
moon), a custom which is still followed in the Islamic positions of the moon, the sun, and the planets in the-
countries. But the first visibility may not occur on field of fixed stars in the months of June and July,*
the predicted day for manifold reasons. 1953.

Fig. 3— Showing the positions of the sun, moon- and planets among the stars in July, j;j53.
The table given on p. 176 is based on mean values The central horizontal line is the line of the

Of the lengths of the year and the synodic month, celestial equator (§ 4.4), and the sinuous line represents
which is equivalent to the assumption that the sun the ecliptic or the sun's path (§ 4.5) but we -mav

181

182

EEPOKT OF THE CALENDAR REFORM COMMITTEE

ignore these now, and simply concentrate on the
moon and the stars or star-clusters near which it
passes.

The moon begins as a thin crescent on the western
horizon on the evening of June 12, the day of the first
visibility after the new-moon, at an angle of 11°, from
the sun which has just set, below the bright stars
Castor and Pollux (Punarvam). Then we notice the
position of the moon on successive evenings at sunset.
We find she is moving eastward at the rate of about
13° and becoming fuller (increasing in phase). She
passes the bright star Regulus (Magha) on the 17th, on
the 19th, she is half and passes Leonis (Uttara
Phalgunt) leaving it a good deal to the north. Then she
passes the bright star Spica ( a Virginis or Citra) on the
21st, and is then gibbous on the 23rd near the star
a-lAbra {Vimkha). Then she passes the well known
Scorpion-cluster and becomes full on the 27th, near
a star-cluster which cannot be seen on the night of
full-moon, but can be detected later as the star cluster
Sagittarius. On the full moon day, she rises nearly
at sunset, at 180° from the sun (opposition). On each
successive night after full moon she rises later and
later, and passes the phases in the reverse order, i.e.,
becomes gibbous on June 30, when she has the bright
star Altair (Srava<na) far to the north and is half on
July 4, and becomes a crescent on July 7 on the eastern
sky, and then fails to appear for three days, and must
have passed the sun on the 11th July which is the new
moon day, when she is with the sun (Amavasya or
conjunction, lit. the Sun and the moon living together).
On the 12th July, she reappears on the western
horizon as a thin crescent, near the star 8-Cancri
{Pusyal and the cycle again starts.

The crescent of the moon, either in the western or
the eastern sky, is always turned away from the sun.

The ancients must have observed the motion of the
moon day after day, fiom new-moon to new-moon
(a full lunation or lunar month) and become familiar
with the stars or star-clusters which she passes. It is
always easy to observe them when the moon is a
crescent ; when the moon becomes fuller, the stars are
lost in the moon's glare particularly if they are faint.
But if observations be carried on for a number of
years, the observers would become familiar with all
the stars or star-clusters which the moon passes.

By observations like this, the ancients must have
found that both the moon and the sun are moving to
the east, the moon very fast, the sun more slowly. By
the time the moon, after making a whole round, comes
back to the sun, the latter has moved further to the
east by about 30°. For example in the above figures
Nos. 2 and 3, the sun was somewhat to the west of the

bright star-group Orionis iMrgosiras) to the west of
Castor and Pollux on Jun; 11th, the day of the new-
moon. But on the next new-moon day, July 11th, she
has moved near Castor and Pollux (Piutarvam) about
30° to the east.

The ancients must have found that the moon takes
a little over 27.3 days (sidereal period of the moon),
to return to the same star, but to overtake the
sun, it takes a little longer, a little over 29.5 days
(the synodic period of the moon). Exactly i

the mean sidereal period -27.321661 days

=27 d 7 h 43 m 11 B .5
with a variation of ± 3J hours
and the mean synodic period = 29.530588 days

= 29 d 12 h 44 m 2 fl .
with a variation of ±7 hours.

The Lunar Mansions :

Many ancient nations developed the habit of
designating the day-to-day (or night-to-night) position
of the moon by the stars or star-clusters it passed on
successive nights. The number of such stars or star-
clusters was either 27 or 28 ; the ambiguity was due
to the fact that the mean sidereal period of the moon
is about 27 £ days, the actual period having a variation
of seven hours, and the ancients who did not know how
to deal with fractions, oscillated between 27 and 28. In
India, originally there were 28 naksatras, but ultimately
27 was accepted as the number of lunar nak?atras
(or asterisms).

The lunar zodiac is also found amongst the Chinese
who designate them by the term Hsiu ; and amongst the-
Arabs, who call them ManxiU both terms denoting man-
sions. Both the Chinese and the Arabs had 28 mansions.
The Indian term 'naksatra* is of uncertain etymological
origin. Some hold that the term nafaatra carried the
sense that 'it does not move* and meant a star.

Names of certain 'naksatras are found in the
oldest scriptures of India, vix., the Rg-Vedas, but a full
list is first found in the Yajurveda (vide § 5 3). In
the older classics of India ( the Yajurveda, the
Mahabharatal the nak$atras invariably star/ with
Kritiket, the Pleiades ; the supposition has been made
that the Kfttikas were near the vernal point, when
this enumeration was started. This is apparent from
the couplet found in the Taittiriya Brahma<na which
runs thus :

Taittiriya Brahmaria, i, 1> 2, 1.

Krttilifi svagnimadadhita

Mukham va etannaksatranarii, Yatkrttika.
Translation : One should consecrate the (sacred)
fire in the Kfttikas y the Kfttikas are the mouth of
the naksatras.

O&LENDARIC AOTBONDMY

183

Later during Siddhanta Jyoti$a times the enumeration
started with Aivini (a? fcA*Mtis)>- and this is still
reckoned to be the first of the naksairas, although the
vernal point has now receded to the UUarabhMrapadd
group which should accordingly he taken as the first
naksatra. But the change has not been done because
the Indian astrologers have failed to correct the
calendar for the precession of equinoxes.

The Chinese start their Hsius with Citra or
a Virginis. This refers probably to the time when
a Virginis was near the autumnal equinoctial point
(285 A.D.). The Arabs start their Manxils with
Arietis (Ash-Sharatani).

There has been a good deal of controversy regarding
the place of origin of the lunar zodiac. Many savants
were inclined to ascribe the origin of the 27 nak^atra
system to ancient Babylon, like all other early astro-
nomical discoveries. But as far as the authors of this
book are aware, there is no positive evidence in favour
of this view. Thousands of clay tablets containing
astronomical data going back to 2000 B.C., and
extending up to the first century A D. have been
obtained, but none of them are known to have any
reference to 27 or 28 lunar mansions.

On the other hand (as mentioned before) some of
the nak§aira names are found in the oldest strata of
the Rg-Vedas {ride § 5 2), which must be dated before
1200 B.C., and a full list with some difference in names
is found in the Yajur-Veda, which must be dated before
600 B.C. Nobody has yet been able, to refute yet Max
Muller's arguments in favour of the indigenous origin
of the Indian nak$alra system given in his preface
to the Rg-Veda Samhita, page xxxv.

It should be admitted that the lunar zodiac was pre-
scientific, i.e., it originated before astronomers became
conscious of the celestial equator and the ecliptic, and
began to give positions of steller bodies with these as
reference planes. The nak$attas give very roughly
the night-to-night position of the moon, by indicating
its proximity to stars and star-groups. Many of the
Indian stars identified as nak$atras are not at all near
the ecliptic or the moon's path which, on account of
its obliquity, is contained in a belt within ±5° of the
ecliptic. Such are for example :

(15) Svatu which is identified with Arcturus
{a Booiis\. which has a latitude of 31° N.

(22) &rava<nu, identified with a, 8, y Aquilae, having
the latitude of 29° N.

(23) &ravis\ha, identified with a, 0, 7l 8 Delphini,
« having the latitude of 33° N.

(25) Purva Bhadrapada identified with a Fegasi and
some other adjacent stars, a Pegasi having latitude of
19° N.

At one time the brilliant star Vega (a Lyme) was
also included making 28 toahsairas. But this has a
latitude of 62° N and was later discarded.

No satisfactory argument has been given for the
inclusion of such distant stars in the lunar zodiac. The
Arabs and the Chinese do not include these distant
stars in their lunar zodiac, but fainter ones near the
ecliptic. Prof. P. C. Sengupta is of the opinion that
Indians generally preferred bright stars, but when such
were not available near the ecliptic, they chose brighter
ones away from the ecliptic, which could be obtained
on the line joining the moon's cusps.

The naksatras were used to name the 'days' in
the earliest strata of Indian literature. Thus when the
moon is expected to be found in the Magha naksaira
(it Leonis), the day would be called the Magha day.
This is the oldest method of designating the day, for it
is found in the Rg-Vedas. Other methods of
designating the day by tithis or lunar days, or by the
seven week-days, came later. The system has continued
to the present times. In old times, astrology was based
almost entirely on the nak§atra$i e.g., in Asoke's records,
the Pusya naksatra day was regarded as auspicious
when Braltiiiavm and Sramanas were fed, in order to
enhance the king's punya (religious merits). In the
Mahabharaia also we find that the days are designated
by naksatras which apparently mean the star or star-
cluster near which the moon is expected to be seen
during the night.

As is apparent from Table No. 5, die naksatras dire
at rather unequal distances, i.e., they rarely follow the
ideal distance of 13 % \ This is rather inconvenient for
precision time-reckoning. We find in the Vedaiiga
Jyotisa times an attempt at a precise definition of the
two limits of a nak$atra, which was detined as 800'
(-13° 20') of the ecliptic. The naksaira was named
according to the most prominent star {Yogatdra)
contained within these limits. These are given in
column (2) of Tabte 5.

We do not, however, have any idea as to how the
beginnings and endings of the naksatra divisions were
fixed in India. The prominent ecliptic stars which were
used as Yogatdras (junction-stars) in pre-Siddhantic
period, are not distributed at regular intervals along
the ecliptic ; and so it was found very difficult to
include the stars in their respective equal divisions.
This will be clear from table (No. 5) where the junction
stars of the naksatras according to the Sunja-
Siddhanta are given in col. (2). The celestial longitudes
of the stars for 1956 A.D. are given in col. (4) and
the beginnings- of each division for the same year are
given in col. (5), taking the star a Virginis tc occupy
the middle position of the naksdtra Oitrd, which marked

184

Nam© of
nakaatras

(1)
Aayipt
Bharani
Krttika
Rohini
Mrgasiras
Ardra
Punarvasu
Pusya
Aslesii
Maghn

Purva Phalguni
Uttara Phalguni
Hasfca
Citra
Svati
Visaklm
Anuradhn
Jyestha
Mula

PurvHsadha
Uttarasadha
Sravana
Dhanistha
Satabhisaj

REPOBT Of THE CALENDAR REEOBM COMMITTEE
Table 5.-fctar s of the Nakaafcra divisions.
Poeitions of the Junction Stars of Naksatra lAviaiona of the Siddhantaa

Beginning point
of the naksatra
division (1956)

(5)

Junction star

Latitude

Longitude

(Yogatard)

S&yana

of naksatra s

(1956)

(2)

(3)

(4)

j3 Arietis

99.'

41 Arietis

i 1U

0.7

4-7

7} Tauri

1 Am

•+■ m

a Tauri

^ a)

0*7

X X

A Orionis

JJSa

a Orionis

ftp
oo

j8 Geminorum

4- A

4-1
ix

1 1 9

S Cancri

4- fi

I u

198

X -lie

a Cancri

1 33

xoo

a Leonis

1 4°,

1 3

8 Leonis

I -L ^

160

(3 Leonis

4-19

1 fi

171

5 Corvi 4 J

— 12

192

a Virginis

— 2

on ^

1 4

x *±

a Bootis

4-30

203

a Libra

224

8 Scorpii

— 1

241

a Scorpii

- 4

249.

\ Scorpii

-13

263

8 Sagittarii

- 6

273

o Sagittarii

- 3

281

a Aquilae

+ 29

301

)3 Delphini

+ 31

315

X Aquarii

340

la a Pegasi

+19

352

la y Pegasi

+ 12

f Piscium

Position of the star
in the naksatra

division.

(6)

h
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18,
19.
20.
21.
22.
23.
24.

25. Purva

26. Uttara

27. Revati

the position of the autumnal equinox at the time
when the table was compiled. The figures in the last
column represent the position of the star in the naksatra
division of that name. It seems that a few of the
Yogataras, viz.. No. 6 Ardra, No. 15 Srati, No. 18
Jye$iha, No. 20 Purvasaiha, No. 21 Uttarasaolha,
No. 22 Sravana, and No. 23 Dhanistha fall outside the
naksatra division of which they are supposed to form the
Yogatara. Matters do not improve much, if we shift
the beginning of each division so as to place ( Fiscium
(Revati) at the end of the Revati division or in
other words at the beginning of the Asriui division.
This will mean that the figures in col. (6) will
then have to be increased by 3° 59', which will
push up the Yogataras of 1 Aivini, 2 Bharani,
3 KrtHka, 8 Pusya, 13 HaSta, 25 P. Bhadrapada, and
26 U. Bhadrapada, so as to go outside the naksatra
division of which they form the Yogatara. In fact no
arrangement at any time appears to have been
satisfactory enough for all the Yogataras to fall within
their respective naksatra divisions.

10°

1 5

1 OQ
lUo

lib

1 4.3

1 5

X 'J

15fi

1 fi°y

1 (33
J.OO

1 *i

A
\j

209

223

236

249

(-)o

263

276

(")2

289

. 55

(")8

303

(-)2

316

(-)o

329

343

356

The divisions of nak^atras shown in the table, as
already stated, has been based on the assumption that
the star Spica occupies the 180th degree of the lunar
zodiac. This arrangement agrees with the statement
of the Vedaitga Jyoiisa that the Dhanis\ha star
(a or j8 Delphini) marked the beginning of the
l)ha>«sthA division, and also of the Varaha's Surya
Siddhanta that Regulus (x Leonis) is situated at the 6th
degree of pe Magha division.

4.2 LONb PERIOD OBSERVATIONS OF THE MOON :
THE CHALDEAN SAROS

The moon gains on the sun at the average rate of
12J° per day, but it did not take the ancients long to
discover that the daily gain of the moon on the sun
is far from uniform ; in fact as we know now, it
varies from approximately 10|° to 14|° per day. It was'
therefore not possible to say beforehand whether
the crescent moon would appear on the 29th or on the
30th day after the beginning of the previous month.

CALENDARIC ASTRONOMY

185

But the exact prediction of the day was a necessity
from the socio-religious point of view. In India, the
month was measured from full-moon to fMl-moon, and
in the Mah&bharata, the great epic which was compiled
from older materials about 400 B. C, it is recorded
that sometimes the full moon occurred on the
thirteenth day after the new-moon, This was taken
to forebode great calamities for mankind. There were
similar ideas in Babylon of which Pannekoek says :

"When the Moon is full on the night of the 14th, the
normal time, it was a lucky omen ; when full-moon happened
on the night of the 13th, 15th or 16th, it wag abnormal,
hence a bad omen. Here astrology and calendar were merged ;
deviation in the calendar was considered an unlucky sign
and had to be restored at the end of the month."*

Neugebauer says :

"The months of the Babylonian calendar are always real
lunar months, the first day of which begins with the first
visibility of the new crescent. The exact prediction of
this phenomenon is the main problem of the lunar theory
as known to us from about 250 B. C. onwards, "t

This is rather comparatively late date. The reason
is that the accomplishment of this objective depends
on the evolution of methods of exact astronomical
observations, and of a method of recording them in
precise mathematical language. Some ancient people
never reached this stage. As far as we are aware,
the ancient Babylonians were the first to evolve
methods of observational astronomy. They also arrived
at the principles of angular measurements, found
the apparent paths of the moon, the sun, and the
planets in the heavens, and discovered that it was only
the sun's path (the ecliptic) which was fixed, and the
paths of the moon, and the planets deviated somewhat
from it. How this was done will be related later.

But even before these accurate methods had been
discovered, the Babylonian astronomers had learnt a
lot more about the moon from long period observa-
tions. The most remarkable of these discoveries is
that of the Chaldean Saros, or a period of 18 years
10J days, in which the eclipses of the sun and the
moon recur.

The occurrence of solar or lunar eclipses, when the
two great luminaries disappear suddenly, either partially
or wholly, were very striking phenomena for the
ancient and medieval people, and gave rise to gloomy
forebodings. There were all kinds of speculations
about the cause of the eclipses, e.g., that the sun and
the moon were periodically devoured by demons or
dragons. The ancient astronomers, however, found
that a solar eclipse takes place only near conjunction

* A. Pannekoek : The Origin of Astronomy.

t G. Neugebauer : Babylonian Planetary Theory.

( new r moon ), but every conjunction of trie stin and
the moon is not the occasion for a solar eclipse. A
lunar eclipse takes place only near opposition (full-
moon ), but every opposition of the sun and the moon
is not the occasion for a lunar eclipse.

In many ancient countries, China and Babylon for
example, records of occurrence of eclipses had been
kept. The celebrated Greek astronomer, Ptolemy of
Alexandria ( ca. 150 A. D. ) had before him a record
of eclipses kept at the Babylonian archives dating
from 747 B. C. They gave date of occurrence, time,
and features of the eclipse, whether they were partial
or total. From an analysis of these records, the
Chaldean astronomers tried to discover the laws of
periodicity of eclipses, which ultimately resulted in the
discovery of the Saros cycle of 18 years and 10 or 11
days. The basis of the Saros cycle is as follows :

We do not exactly " know when the ancient
astronomers outgrew the myth of demons periodically
devouring the sun and the moon during eclipse times,
and arrived at the physical explanations now known
to every student of astronomy, and reproduced in the
diagrams given below.

Fig. 4— Showing an eclipse of the moon.

But when they arrived at physical explanation of
ellipses, they had an understanding as to why there
are no eclipses during every full moon and new moon.
The paths of the two luminaries must be in different
planes. This we take up in a subsequent section more
fully, when we describe how the sun's path or ecliptic
was discovered.

Suffice it to say that at some ancient epoch, some
Chaldean astronomer discovered that the moon's path
was different from the sun's, and therefore cuts the
sun's path at two points, now called Nodes. The
condition for an es&pse to happen is that the full-
moon and new-moon must take place sufficiently close
to the Nodes, otherwise the luminaries would be too
far aipart, for an eajipse to take- place. -

The 'Nodes* now take the place of the mythical dra-
gons which were supposed to waylay the sun and the
moon, periodically, and swallow and disgorge them.
In Hindu astronomy, the ascending node is called

186

REPORT OF THE CALENDAR' REFORM COMMITTEE

Hcchu with the symbol arrd the descending' node is
called' Keiu with the symbol ft, the names of the two

month, because the nodes regress to the west. Its
value is 27.21222 days.

APPEARS SMALLER
THAN SUN

EARTH

Fig. f> — Showing an annular eclipse ot the sun.

halves of the demon, who was cut in two by gods, so
that the sun and the moon could get out.

In very ancient times, it was found that the two
'Nodes' were not fixed, but moved steadily to the west,
so that the sun took less than a year to return to the
same node. This time is known as the * Draconitic year'
or year of the Dragons, and its length is 346.62005
days. The time in which the moon returns to the
same node is known as the draconitic month or the
month of dragons. It is slightly less than the sidereal

Table 6. — List of Lunar

EARTH

Fig. 6— Showing a total eclipse of the sun.

The Chaldeans appear to have found, about 400
B. C, that 223 synodic months = 242 draconitic months.

The reader can verify

223 synodic month =6585.321 days
242 draconitic months — 6585.357 days

From their long observations of eclipses, the
Chaldean astronomers must have found that eclipses
recur after an interval of 6585 J days or 18 years llf
days (or 18 years 10 J days if 5 leap-years intervene).
This cycle has been known as the Chaldean Saros*
The extent to which a knowledge of the cycle is useful
is given in the following modern table.

Eclipses of the Sa,ros cycle.

Lunar Eclipses

1914, Mar.

1932, Mar.

1950,

Apr.

Asc.

Part. -Total

Sept.

Des.

Part.-Total

1916, Jan.

1934, Jan.

1952,

Feb.

Asc.

Partial

July

Aug.

Des.

Partial

1917, Jan.

1935, Jan.

1953,

Jan.

Asc.

Total

July

Des.

Total

Dec.

1936, Jan.

1954,

Jan.

Asc.

Total

1918, June

July

Des.

Partial

1919, Nov.

1937, Nov.

1955,

Nov.

Asc.

Partial

1920, May

1938, May

1956,

May

Des.

Total-Part.

Oct.

Nov.

Asc.

Total

1921, Apr.

1939, May

1951,

May

Des.

Total

Oct.

Nov.

Asc.

Part.-Total

1923, Mar.

1941, Mar.

1959,

Mar.

Des.

Partial

Aug.

Sept.

Asc.

Partial

1924, Feb.

1942, Mar.

1960,

Mar.

Des.

Total

Aug.

Sept.

Asc.

Total

1925, Feb.

1943, Feb.

1961,

Mar.

Des.

Partial

Aug.

Asc.

Part.-Total

1927, June

1945, June

1963,

July

Asc.

Total-Part.

Dec.

Dec

Dec.

Des.

Total

1928, June

1946, June

1964,

June

Asc.

Total

Nov.

Dec.

Des.

Total

1947, June

1965,

June

Asc.

Partial

1930, Apr.

1948, Apr.

Asc.

Partial

Oct.

Des.

Partial

1931, Apr.

1949, Apr.

1967,

Apr.

Asc.

Total

Sept.

(Jet.

Oct.

18-

Des.

Total

CALENDABIC ASTBONOMY

187

Table 7.— List of Solar Eclipses.
Eclipses of the Saros cycle

Solar Eclipses

The dates of recurrence of the corresponding eclipses in three cycles from 1914 to 1967, the node at which
the eclipse occurs, and the nature of the eclipse are shown below.

1914, Feb.

1932, Mar.

1950, Mar.

Asc.

Annular

Aug.

Sept.

Des.

Total

1915, Feb.

1933, Feb.

1951, Mar.

Asc.

Annular

Aug,

Aug.

Sept.

Des.

Annular

1916, Feb,

1934, Feb.

1952, Feb.

Asc.

Total

July

Aug.

Des.

Annular

Dec.

1935, Jan.

1953, —

Asc.

Partial

1917, Jan.

Feb.

Asc.

Partial

June

July

Des.

Partial

July

Aug.

Des.

Partial

Dec,

Dec.

1954, Jan.

Asc.

Annular

1918, June

1936, June

June

Des.

Total

Dec.

Asc.

Annular

1919, May

1937, June

1955, June

Des.

Total

Nov.

Dec.

Asc.

Annular

1920, May

1938, May

1956, June

Des.

Part .-Total

Nov.

Dec.

Asc.

Partial

1921, Apr.

1939, Apr.

1957, Apr.

Des.

Annular

Oct.

Asc.

Total-Part.

1922, Mar.

1940, Apr,

1958, Apr.

Des.

Annular

Sept.

Oct.

Asc.

Total

1923, Mar.

1941, Mar.

1959, Apr.

Des.

Annular

Sept.

Oct.

Asc.

Total

1924, Mar.

1942, Mar.

1960, Mar.

Des.

Partial

July

Aug.

—

Asc.

Partial

Aug.

Sept.

Asc.

Partial

1925, Jan.

1943, Feb.

1961, Feb.

Des.

Total

July

Aug.

Asc.

Annular

1926, Jan.

1944, Jan.

1962, Feb.

Des.

Total

July

Asc.

Annular

1927, Jan.

1945, Jan.

1963, Jan.

Des.

Ann. -Total

June

July

Asc.

Total

Dec.

1946, Jan.

1964, Jan.

Des.

Partial

1928, May

May

June

Asc.

Total-Part.

June

July

Asc.

Partial

Nov.

Dec.

Des.

Partial

1929, May

1947, May

1965, May

Asc.

Total

Nov.

Des.

Annular

1930, Apr.

1948, May

1966, May

Asc.

Ann.-Total

Oct.

Nov.

Des.

Total

1931, Apr.

1949, Apr.

1967, May

Asc.

Partial

Sept.

Des.

Partial

Oct.

Nov.

Des.

Part.-Total

The problem of first visibility of the moon £ with the sky were discovered in ancient times. This is
which we started cannot therefore be taken up unless taken up in the succeeding sections,
we describe how the path of the sun and the moon in

C. £.—32

188

BEPOUT OF THE CALENDAR REFORM COMMITTEE

4.3 THE GNOMON

Observations of the positions of the sun, the moon,
planets and stars are now made very accurately with
elaborate instruments installed in observatories. But
these instruments have been evolved after thousands
of years of experience and application of human
ingenuity, and have undergone radical changes in
design and set-up with every great technological
discovery. But let us see how the early astronomers
who had no instruments or very primitive ones made
observations, collected the fundamental data, and
evolved the basic astronomical ideas.

The earliest instrument used by primitive astrono-
mers appears to have been the gnomon, which we
now describe.

Fig. 7— The gnomon

The ancients determined the latitude of the place, obliquity
of the ecliptic, the length of the year and the time of day by
measuring the length and direction of shadow of the gnomon.
The figure ehows the noon-shadow of the gnomon AB, AE
being the equinoctial shaoow and AO and AD the shadow on
two solstice-days, at a place on latitude - 0.

Nobody can fail to see the change in direction
and length of shadows of vertical objects throughout
the day-time, and throughout the year. When these
observations are carefully made, by means of the
gnomon ( &anku in Sanskrit ), which is simply a
vertical stick planted into the ground, and standing
on fairly level ground of large area, without obstruc-
tions from any direction, a good deal of astronomical
knowledge can be easily deduced. These observations
appear to have been made in all ancient countries.

We have the following description, by George
Sarton, of observations made in ancient times in
Greece with the aid of the gnomon.*

"It (the gnomon) is simply a stick or a pole planted
vertically in the ground, or one might use a column built for
that purpose or for any other ; the Egyptian obelisks would
have been perfect gnomons if sufficiently isolated from other
buildings. Any intelligent person, having driven his spear

* Sarton mentions Anaximander ( c 610-545 B.C.) of Miletus as the
earliest Ionian philosopher who used the gnomon in Greater Greece.

into the sand, might have noticed that its shadow turned
around during the day and that it varied in length as it
turned. The gnomon in its simplest form was the
systematization of that casual experiment. Instead of a
spear, a measured stick was established solidly in a vertical
position in the middle of a horizontal plane, well smoothed
out and unobstructed all around in order that the shadow
could be seen clearly from sunup to sundown. The astro-
nomer (the systematic user of the gnomon deserves that
name) observing the shadow throughout the year would see
that it reached a minimum every day (real noon), and that
minimum varied from day to day, being shortest at one time
of the year {summer solstice) and longest six months later
{winter solstice^. Moreover, the direction of the shadow
turned around from West to East during each day,
describing a fan the amplitude of which varied througout
the year"'.*

From the observation of the shadows cast by the
gnomon, many useful deductions could be made.
These are : —

(1) Mark the points in the morning and in the
evening when the shadows are equal in length and
draw the lines showing the shadows. Then bisect
the angle between the two shadow lines. This gives
us the meridian or the north-south direction of the
place.

The process of bisection was done by taking a rope
attaching extreme points to the end points of the
equal shadows ; then take the mid-point of the rope,
and stretch the rope, and mark the position of
the mid-point. This connected to the pole gives us
the meridian line. If we draw a circle, with the pole
as centre, and draw the meridian, the point where it
strikes the northern semi-circle is the North point,
opposite is the South point. The East and West
points are found by drawing a line at right angles to
the north-south direction.

So the cardinal directions are found.

(2) Observe the position of the sunrise from day
to day. If observations are carried on throughout the
3'ear, there will be found two days in the year when
the sun will arise exactly on the east point. Then it
is found that the day and night are equal in length.
These days are called the Equinoctial days. Let us
start from the equinoctial day in Spring (vernal
equinox). This happens on March 21st. Then we
observe that the sun at sunrise is steadily moving to
the north, at first rapidly, then more slowly. Near
the extreme north, the sun's movement is very slow,
so this point is called the 'Solstice which means the
sun standing still. Actually the sun reaches its
northern-most point on June 22 (summer solstice).

* George Barton : A History of Science, p. 174.

CALENDABIC ASTRONOMY

189

The day is longest on this date. Then the sun begins to
move south till it crosses the east point on September
23, when day and night again become equal (the autum-
nal equinox day). It continues to move south, till
the extreme south is reached on December 22, (the
winter solstice day), when daylight is shortest for
places on the northern hemisphere. Then the sun
turns back towards the east point reaching it on
March 21, and the year-cycle is complete.

The gnomon thus enabled the ancient astronomers
(in Babylon; India, Greece, and China) to determine :

(a) The Cardinal points : Fast, North, West, and
South ; the north-south line is the meridian line (the
Yamyottaia-rekha in Indian astonomy).

(b) The Cardinal days of the Year : vix.,

The Vernal Equinox (V.E.) day, when day and
night are equal.

The Summer Solstice (S.S.) day, when the day
is the longest for observers on the northern hemisphere.

The Autumnal Equinox (A.E.) day, when day
and night are again equal.

The Winter Solstice (W.S.) day, when the day
is the shortest for observers on the northern hemisphere.

All early astronomical work was done in the
northern hemisphere.

These methods are fully described in the Surya-
ShWianta, Chap. Ill, but they appear to have been
practised from far more ancient times. In the
appendix (5-C), we have quoted passages from the
Aitareija Brahmana which shows that the gnomon was
used to determine the cardinal days of the year at the
time when this ritualistic book was compiled. The
date is at least 600 B.C., i.e., before India had the
Greek contact. It may be considerably older even.

(c) To mark out the Seasons : We have
mentioned earlier that in countries other than Egypt,
there were no impressive physical phenomenon like
the arrival of the annual flood - of the Nile to mark
the beginning of the solar year, or of the seasons. The
seasons pass imperceptibly from the one to the other.

The gnomon observations probably enabled the
early astronomers of Babylon and Greece to define the
onset of the seasons, and the length of the year with
greater precision.

In Graeco-Chaldean astronomy, we have four
seasons :

Spring from V.E. to S.S.

Summer S.S. to A.E.

Autumn*- „ A.E. to W.S.

Winter- „ W.S. to V.E.
Thus every season starts immediately after a
cardinal day of t,he year and ends on the next
cardinal day.

According to Neugebauer :

"Babylonian astronomy ( during Seleucid periods,
300 B.C. -75 A.D. ) waa satisfied with an exact four-division
of the seasons as far as solstices and equinoxes are

concerned, with the summer solstice ( and not the vernal

point ) as the fixed point."*

At a later stage, they however found that the four
seasons had unequal lengths ( vide § 3*1).

The above definition of 'seasons' has come down
to modern astronomy. The Hindu definition of
seasons was different ( vide § 5-6 and 5-A )

The observation of the Cardinal days of the year
appear to have been carried out all over the ancient
world by other methods, and often in a far more
elaborate manner. People would observe the
day-to-day rise of the sun on the eastern horizon, and
mark out the days when the sun was farthest north
(summer solstice day), or farthest south (winter solstice
day). The time period taken by the sun to pass from
the southern solstitial point to the northern solstitial
point was known in the Vedas as the Uttardyana
(northern passage), and that taken by the sun to pass
from the northern solstitial point to the southern
solstitial point was known as the Daksinayana
(southern passage). Exactly midway between these
points the sun rises on the vernal and autumnal
equinoctial days. From the passage in the fcatapatha
Brahma^ quoted later ( vide §53), we see clearly that
the point on the eastern horizon, where the sun rose
on these days, was recognized to be the true east.

Doubt has been expressed about the ability of
Vedic Aryans to make these * observations, but to these
objections, B. G. Tilak replied in his Orion, pp. 16-17.

"Prof. Weber and Dr. Schrader appear to doubt the
conclusion on the sole ground that we cannot suppose the
primitive Aryans to have so far advanced in civilization
as to correctly comprehend such problems. This means
that we must refuse to draw legitimate inferences from
plain facts when such inferences conflict with our precon-
ceived notions about the primitive Aryan civilization. I
am not disposed to follow this method, nor do I think that
people, who knew and worked in metals, made clothing
of wool, constructed boats, built houses and chariots,
performed sacrifices, and had made some advance in
agriculture, were incapable of ascertaining the solar
and the lunar years. They could not have determined it
correct to a fraction of a second as modern astronomers
have done ; but a rough practical estimate was, certainly,
not beyond their powers of comprehension. *

The best example of the ability of the ancient
people to observe the cardinal points of the sun's
motion is afforded by the Stonehenge in the Salisbury
plains of England, of which detailed accounts

* Neugebauer : Babylonian Planetary Theory, Proc. Amer. Philoa.
Soc. Vol. 98 : 1, 1954, p. 64.

190

REPOBT OF THE CALENDAR BEFOBM COMMITTEE

have recently appeared in Scientific American ( 188,
6-25, 1953 ) and Discovery (1953, Vol. XIV, p.276).

It is related in these two publications, that not a
long time subsequent to 1800 B.C., say about 1500-1200
B.C., the then inhabitants of Britain, who had not even
learnt the use of any metal, but used only stone
implements, could construct a huge circular area
enclosed by large upright monoliths forming lintels
and with a horse-shoe shaped central area having its
axis in the direction of sunrise on the summer solstice
day. It has been proved, almost beyond any doubt,
that the Stonehenge was used for the ceremonial
observation of sunrise on this day. Sir Norman
Lockyer in 1900 found that the direction of the axis of
the horse-shoe actually makes an angle of about H° with
the present direction of sunrise on the summer solstice
day. He did hot think that it was a mistake on the
part of the original builders ; but that on account
of the change in obliquity (angle between equator and
ecliptic), the present direction of sunrise had changed
to the extent of H° and using the rate of change of
obliquity, he could fix up the time of construction at
1800 ± 200 B.C. This estimate has been brilliantly
confirmed by C 14 -analysis of some wood charcoal
found in the local burial pits which are presumed to be
contemporary with the erection of the Stonehenge.

After this brilliant confirmation of Lockyer's
hypothesis, it is hoped that there will be less hesitation
on the part of scholars to admit that it was possible
for the Vedic Aryans who knew the use of metal and
were far more advanced than the stone-age people of
Britain, to devise methods for the observation of the
cardinal points of the year.

How did they observe these points ? Probably in the
same way as the Britishers of 1500 B.C., by observing
from a central place, the directions of sunrise on the
eastern horizon throughout the year. The directions
of the solstitial rises could be easily marked. Probably
the equinoctial points were found by bisecting the
angle between these two directions by means of ropes
as described in the Sulva- Sutras.

4.4 NIGHT OBSERVATIONS : THE CELESTIAL
POLE AND THE EQUATOR

Almost all ancient nations were familiar with the
night-sky either as shepherds, travellers or navigators,
and were acquainted with more detailed knowledge
of the revolving blue firmament studded with stars
than the modern city dweller. The striking constell-
tions like the Great.Bear, the Pleiades, the Orion could
not but catch their fancy and references to these star-
groups arc found in ancient literature, in the Vedas, m

the book of Job (the Bible) and in Homer. In the last,
the star-groups are used by sailors to find out their
orientation. Representations of star-groups are found
in ancient Babylonian boundary stones of about
1300 B.C. (see Fig. 15).

Let us now see how these observations were
made.

Suppose, on a clear moonless evening in early
Spring (say March ) and at about 8-30 P.M., we take
our stand in a wide field undisturbed by city lights,

NORTH
i

HORIZON

Fig. 8-Showing the positions of Ursa Major (Saptar.fi) at
interval of 3 hours.

and our vision is unobstructed in all directions. We
now face the north. We shall find the appearance
of the heavens as shown in Fig. (8) :

In the north, a little high up to our right hand
side we cannot fail to observe the conspicuous
constellation of seven stars, called in Europe the
Great Bear, but in India, the Saptanti or seven seers.
If we observe the heavens 3 hours later, we shall
observe that the group has changed its position as
shown in Fig. (8). Let us fix our attention on the
two front stars (the pointers) of the Great Bear
and join a line through them. The line joining these
two stars appear to behave like the hands of a watch,
for if produced they pass through a star half as bright
at some distance, and appear to have revolved about it
as centre. This star is called the Pole Star or Polans,
or Dhruva in Sanskrit which means fixed. If we
observe throughout the night, we shall find that the
Polaris remains approximately fixed, and the line of
pointers continues to go round it. The next day, at

CALENDARIO ASTRONOMY

191

8-26 P.M., nearly 24 hours later they are again almost
exactly at the same position.

We naturally come to the conclusion that the
whole starry heavens have been rotating round an
axis passing through the observer and the Pole Star
from east to west, and the rotation is completed in
nearly 24 hours (exactly 23 h 56 m 4 8 of mean solar time).

Definition of the Poles

The celestial poles, or the poles round which
the rotation of the celestial sphere takes place may .
therefore be defined as those two points in the sky
where a star would have no diurnal motion. The
exact position of either pole may be determined with
proper instruments by finding the centre of the small
diurnal circle described by some star near it, as for
instance, the stars belonging to the Ursa Minor group.
Actually the so-called pole star is at present 57
minutes away from the correct position of the pole
which is not actually occupied by any star.

Since the two poles are diametrically opposite in
the sky; only one of them is usually visible from a
given place : observers north of the equator see only
the north pole, and vice versa in the southern
hemisphere. The south pole is not marked by any
prominent star.

Knowing as we now do, that the apparent revolu-
tion of the celestial sphere is due to the rotation of
the earth on its axis, we may also define the poles as
the two points where the earth's axis of rotation (or
any set of lines parallel to it), produced indefinitely,
would pierce the celestial sphere.

The Celestial Equator and Hour Circles

The celestial equator is the great circle of the
celestial sphere, drawn halfway between the poles

Z R

Fig. 9— The celestial sphere.

(and therefore everywhere 90° from each of them), and
is the great circle in which the plane of the earth's
equator cuts the celestial sphere, as illustrated in
Fig, (9). Small circles drawn parallel to the celestial

equator, like the parallels of latitude on the earth,
are called parallels of declination. A star's parallel of
declination is identical with its diurnal circle.

The great circles of the celestial sphere, which pass
through the poles in the same way as the meridians on
the earth, and which are therefore perpendicular to
the celestial equator, are called hour-circles. Each
star has its own hour-circle, which at the moment
when the star passss the north-south line through the
zenith of the observer, coincides with the celestial
meridian of the place.

4.5 THE APPARENT PATH OF THE SUN IN THE SKY :
THE ECLIPTIC

The apparent path of the sun in the sky is known
in astronomical language as the ecliptic. It is a great
circle cutting the celestial equator at an angle of ca
23J° (exactly 23° 26' 43" in 1955, but the angle varies
from 22° 35' to 24° 13'). This is known as the
obliquity of the ecliptic.

The ecliptic is the most important reference circle
in the heavens, and let us see how a knowledge of it
was obtained in ancient times.

It is obvious that a knowledge of the stars marking
the sun's path could not be obtained directly as in the
case of the moon ; for when the sun is up, not even
the brightest stars are visible. The knowledge must
have been obtained indirectly. Early observers were
accustomed to observe the heliacal rising of stars, i.e.,
observe the brilliant stars lying close to the sun which
are on the horizon just before sunrise. This must
have given them a rough idea of the stars lying close to
the sun's path. From these observations, as well as
from successive appearances of the moon on the first
days of the month as narrated in § 41, they must have
also deduced that the sun was slipping from the west
to the east with reference to the fixed stars, and
completing a revolution in one year. But how ivas
this path rigorously fixed ?

It appears that a knowledge of the stars lying on,
or close to the moon's path was obtained from observa-
tions made during lunar, rarely of solar eclipses.

They must have realized, as narrated in § 4.2,
that during a total lunar eclipse, the moon occupies a
position in the heavens opposite the sun, and the stars
close to the moon, which become visible during
totality, approximately mark out points on the sun's
path. So the word * Ecliptic* which means the locus of
eclipsas, came to denote the sun's path.

The two points of intersection of the ecliptic
with the celestial equator are called respectively the

192

KEPOBT OF THE CALENDAR REFORM COMMITTEE

Firsi point of Aries, and the First point of Libra. The
first point of Aries is the ascending node, when the
sun passes from the south to the north > the first
point of Libra is the descending node, when the sun
passes from the north to the south. We have vernal
equinox when the sun is at the first point of Aries,
summer solstice when the sun is at the first point of
Cancer, autumnal equinox when the sun is at the first
point of Libra, and winter solstice when the sun is
at the first point of Capricorn. To the origin of
nomenclature, we return later.

The celestial equator and the ecliptic are the most
important reference planes in astronomy. The
positions of all heavenly bodies are given in terms of
these planes, taking the first point of Aries as the
initial point. We explain below the scientific defini-
tions of spherical co-ordinates used to denote the
position of a body on the celestial globe.

Fig. 10.— Stowing the spherical co-ordinates of a «ar.

In this figure :

P= Celestial pole (dhnud).
rQi. =• Celestial equator.

K>Pole of the ecliptic (kadamba).
X s = Plane of the ecliptic.
T = First point of Aries (vernal equinox),
s = First point of Cancer ( summer solstice).
^ = First point of Libra (autumnal equinox).
Vf «= First point of Capricorn (winter solstice).
S = A heavenly body.
PS^=Great circle thro'P,S cutting equator at Q.
rQ^Right ascension — a
QS« Declination *S

KS^ Great circle through K, S cutting ecliptic
at C.

rC« Celestial longitude « X
CS ~ Celestial latitude = p
Let PS cut the ecliptic at B. Then
rB K Polar longitude or dhruvaka = I
BS=* Polar latitude or vik$epa=*d
These last two peculiar co-ordinates, now no longer
used, were used by the Surya Siddhanta to denote star
positions. They have been traced by Neugebauer to
Hipparchos five centuries earlier.

The position of a stellar body may be defined by
either its right ascension (a) and declination (8),
or its celestial longitude(x) and latitude(0).
The positions of stars in these co-ordinates began to
be given from the time of Claudius Ptolemy (150 A.D.)
who used them in his Syntaxis.

4 6 THE ZODIAC AND THE SIGNS

The early astronomers must have found that the
sun's path in the heavens was almost fixed, while
that of the moon, and of the planets, which acquired
for astrological reasons great importance from about
1200 B.C., strayed some degrees to the north and south
of the ecliptic.

In case of the moon the deviation from the ecliptic
was found to be not much greater than 5°, but some
of the planets strayed much more; in. the case of
Venus, her perpendicular distance from the ecliptic
rises sometimes as high as 8° degrees. So a belt was
imagined straying about 9° north and 9° south of the
ecliptic, in which the planets would always remain in
course of their movement. This belt came to be
known as the 'Zodiac*

The complete cycle of this belt was divided into 12
equal sectors each of 30°, and each sector called a
'Sign'. The signs started with one of the points of
intersection of the ecliptic and the equator, and the
first sign was called " Aries* after the constellation of
stars within it. The names of the succeeding signs are
given in Table No. 8 on the next page, in which :

The first column gives the beginning and ending of
the signs, the vernal equinoctial point being taken as
the origin. r

The second column gives the international names
which are in Latin with the symbols used to denote
the signs.

The third column gives their English equivalent.

The fourth column gives the Greek names. They
are synonimous with the international names.

The fifth column gives a set of alternative name*
for the signs given by Vartthamihira.

CALENDARIC ASTBONOMY

193

Table 8 —Zodiacal Signs.
Different Names of Zodiacal Signs

Beginning and Name of the English Greek

ending of the Signs & equivalent names

Signs Symbol

(1) (2) (3) (4)

0°- 30° T Aries Bam Ki-ios

30 - 60 B Taurus Bull Tauros

60 - 90 n Gemini Twins Didumoi

90 -120 s Cancer Crab Karxino;

120 -150 Q. Leo Lion Leon

150 -180 11 JP Virgo Virgin Parfchenosj

180 -210 . ■ ^ Libra Balance Zugos

210 -240 i'l Scorpio Scorpion Scorpios

240 -270 t Sagittarius Archer Tozeutes

270 -300 V/ Capricornus Goat Ligoxeros

300 -330 - Aquarius Water Bearer Gdroxoos

330 -360 K Pisces Fish Ichthues

The sixth column gives the Indian names.
The seventh column gives the Babylonian names.
It can be easily inferred from the table that the
names are of Babylonian origin, but their exact
significance is not always known. It has been assumed
that the symbols used to denote the signs have been
devised from a representation of the figure of the
animal or object after which the sign has been named,
for example, the mouth and horns of the Ram, the same
of the Bull, and so on.

It is seen that Varahamihira's alternative names
given in column ( 5 ) are simply the Greek names
corrupted in course of transmission and as adopted for
Sanskrit ; with the exception of the name for
Scorpion, which is given as l Kaurpa". This has phonetic
analogy' with the corresponding Babylonian sign name
Akrabu for Scorpion. The purely Sanskrit names
given in column (6) are all translations of Greek names
with the exceptions of :

(3) Twins, which become Miihuna or Amorous
couple',

(9) the Archer, which becomes the 'Bow',

(10) the Goat, which becomes the 'Crocodile',

(11) Water bearer, which becomes the 1 Waterpot'.
Some of them appear to have been translations of
Babylonian names.

The Babylonian names, as interpreted by Ginzel*
are given in the seventh column, with their meanings.

It is thus seen that the names of the zodiacal signs
are originally of Babylonian origin. They were taken
over almost without change by the Greeks, and
subsequently by the Romans, and the Hindus, from
<Graeco-Chaldean astrology.
* Giazdi Handbuch der Mathematischen- unci Technischm Chrono-
loati. Vol. I, P, 84.

Varaha
Mihira

Kriya

Taburi

Jituma

Kuli r a

Leva

Pathona

Jiika

Kaurpa

Tanks ika

Akokera

Hrdroga

Antvabha

Indian
names

(6)

Mesa,

Vrsibha

Mithuna

Karka or Karkata

Sim ha

Kanya

Tula

Vi/seika

Dhanuh

Makara

Kumbha

Mlna

Babylonian
names

(7)

Ku or Iku (Earn)
Te-te (Bull)
Masmasu (Tsvins)
Nangaru (Crab)
Aru (Lion)
Ki (Virgin)
Nuru (Scales)
Akrabu (Scorpion)
Pa (Archer)
Sahu (Goat)
Gu (Water carrier)
Zib (Fish)

But why was such an odd
names chossn for the 'Signs'
interesting speculations. The

assortment of animal
? There have been
reader may consult
Brown's Researches into the Origin of Ike Primitive
Constellations of the Greeks, Phoenicians and Babylonians,
London, 1900.

These signs were taken up by almost all nations in
the centuries before the Christian era on account of
the significance attached to them by astrologers. In
Greece, they were first supposed to have been
introduced by the early Greek astronomer Cleostratos,
an astronomer who observed about 532 B.C. in the
island of Tenedos off the Hellespont who introduced
the designation 'Zodiac* to describe the belt of stars
about the ecliptic. The twelve 'Zodical Signs' are
not known in older ritualistic Indian literature like
the Brahmanas. They appear to have come to India
in the wake cf the Macedonian Greeks or of nations
like the Sakas who were intermediaries for trans-
mission of Greek culture to India.

Confusion in the starting point of the Zodiac

The Initial Point' of the zodiac should be the
Vernal Point or the point of intersection-of the ecliptic
and the equator, but as will be shown in the next
section, this point is not fixed, but moves west-ward
along the ecliptic at the rate of approximately 50- per
year (precession o£ the equinoxes). This motion is
unidirectional, but bsfore Newton proved it to be so in
1687 from dynamics and the law of gravitation, there
was no unanimity even among&t genuine astronomers
about the uni-directional nature of precessional
motion, inspite of overwhelming observational
evidences.

194

BEPORT OF THE CALENDAE BEFORM COMMITTEE

The hesitation of the medieval astronomers in
accepting precession can be easily understood. Most
of them earned their livelihood by practising the
'Astrological Cult' which was reared on the basis that
the signs of the zodiac are fixed, and coincident with
certain star-groups ; but this assumption crumbles to
the ground if precession is accepted. But as historical
records now show, though astronomers had clearly
recognized that the initial point should be the point
of intersection of the equator and the ecliptic, there
was no unanimity even amongst ancient astronomers
of different ages regarding the location of this
point in the heavens, because it was not occupied by
any prominent star at any epoch and the ancients
were unaware of the importance of its motion
(vide § 4-9).

4.7 CHALDEAN CONTRIBUTIONS TO ASTRONOMY :
RISE OF PLANETARY AND HOROSCOPIC ASTROLOGY

We have seen that it was the needs of the
calendar which gave rise to scientific astronomy—
which in the earliest times covered :

.MOV. 24

The attention of mankind was drawn in remote
antiquity to the five star-like bodies :

Venus, Jupiter, Mars, Saturn and Mercury.

Venus and Jupiter and occasionally Mars are more
brilliant than ordinary stars. Sooner or later it was
found that while the ordinary stars remain fixed on
the revolving heavens these five stars creep along
them, as a modern author puts it, 'like gloio-ivorms
on a ivhirling globe', each in its own way. Venus
appears as a morning and evening star, the maximum
elongation being 47°. It early drew the attention of
'sea-faring people, its appearance on the eastern horizon
indicating early sunrise to persons on lonely seas.
But it took mankind some time to discover that it was
the same luminary which appeared for some period as
a morning star, then as an evening star. Its brilliance
could not but strike the imagination of mankind.
Mercury also appears regularly as morning and evening
star, and it must have been discovered later than
Venus, but still at such a remote age in antiquity that
all traces of its discovery are lost.

The motion of the brilliant luminary, Jupiter
across the sky attracted early attention ; Mars

MAR. £4

The Path of Mart Among the Stars in 1939.

Fig. 11— Showing the retrograde motion of Mars.
Although the planets always move in the same direction round the suti, their: apparent motion among
the fixed stars as seen from the earth, is not always in the same forward direction. They sometimes
appear to move also in the backward direction among the stars, and this is known as the retrograde
motion of a planet. The above figure reproduced from Pictorial Astronomy by Alter and Cleminshaw
illustrates how Mars was seen to retrograde during June 24 to August 24.

(a) Systematic observation of the movements of
the moon, and the sun,

(b) Recording of the observations in some
convenient form on permanent materials,

It is not, however, correct to say that it was the
calendar based on the sun and the moon which
provided tfae sole stimulus for astronomical studies.
fa one t&ftft, "the planets strongly captured the attention

rim*?*

/ A. Pjg$#<^C0ek : Origin of Astronomy, p. 351.

occasionally bursts into brilliance with fierce, red
light, which could not but attract notice. The three
planets, Mars, Jupiter, and Saturn though generally
moving to the east, from time to time reverse their
direction of motion (retrograde motion), as shown
in Fig. 11.

From very early times and amongst widely
separated communities, mystifcal importance was
ascribed to the wandering of the Janets.

These mystical ideas took & very definite form in
the shape of 'Planetar^ AslroUW which grew in
Mesopotamia dUring the period B.C. to 800 B.C.
This Planetary Astrology i* *» m distinguished from

CALENDAEIG ASTRONOMY

195

an older form of Astrology widely found in Vedic
India, which centred mainly round the moon, and the
lunar mansions, and to a lesser extent on the sun.
The conjunction of the moon with certain nak$atras
was considered lucky, others unlucky (vide § 4'1).

Planetary Astrology took the world by the
storm after 300 B.C. and its influence was strongest
during middle ages in Europe, till the rise of
rationalism and modern science almost completely
undermined this influence. But it still survives amongst
the credulous in the West, but to a far greater extent
than amongst the eastern nations.

emerged in Babylonian history from the time of
Assyrian supremacy (ca. 1300 B.C.), for these appeared
to be linked up with the mysteries of Heaven itself,
and the astrologer enjoyed very great prestige amongst
the public, for did he not possess the mysterious power
of foretelling correctly the dates of eclipses !

Here are some of the samples o£ astronomical
omina during the last centuries of Assyrian power
(900 B.C.-600 B.C.).

"Mercury went back as far as the Pleiades' 1 ; "Jupiter
enters Cancer" ; "Venus appears in the East" ; "Mars is
very bright" ; "Jupiter appears in the region of Orion" ;

EAST

Fig. 12— Showing the motion of Mars relative to the earth.

By placing the sun at the centre and having the earth and the other planets revolve in circles around
it Copernicus (1473-1543) was able to explain the backward motion of the planets among the stars much
more simply than in the Ptolemaic system. This is illustrated in the above figure, taken from Phonal
Astronomy, in the case of Mars as seen from the earth. The earth's speed is IB* miles a second while that
of Mars is onlv 15 miles a second. As the earth overtakes Mars, the latter seems to move backward The
direct motion of Mars to the east is shown at positions 1, 2 and 3, backward or retrograde motion to the
west at 4 and 5, and direct motion to the east again at 6 and 7.

What was the reason for the strong fascination
which man has for astrology ?

Mankind has always a psychological weakness
for omina, i.e., some signs which can predict future
events, good or bad. The older form of omina
were rather crude, viz., flight of certain birds like the
crow, or movements of animals like the jackal or the
snake, howlings of certain birds and animals. In many
countries, sheep and goats were sacrificed to gods on
the eve of great enterprises, and Augurs claimed to
be able to interpret the intentions of the gods
from an examination of lines and convolutions on
the liver of the sacrificial animal ( fiepatoscopy ).
Meteorological phenomena such as a lightning
discharge, haloes round the moon, aurora were also
regardefas 'omens'.

The older forms of omina were all apparently very
crude compared to planetary omina which gradually

"Mars stands in Scorpio, turns and goes forth with
diminished brilliancy" ; "Saturn has appeared in the Lion" ;
"Mars approached Jupiter" ; and so on.

There is not a trace of scientific interest in these texts ;
the mind of the reporters is entirely occupied by the omens :
When such or such happens,

"it is lucky for the king, my lord" ;

or, "copious floods will come" ;

"there will be devastation" ;

"the crops will be diminished" ;

"the king will be besieged" ;

"the enemy will be slain" ;

"there will be raging of lions and wolves" ;

"the gods intend Akkad for happiness" ;

and so on.

Yet, with all those observations, these reports represent
a considerable astronomical activity. For the first time
in history a large number of data on the planets had been

C.R.— 33

196

REPORT OF THE CALENDAR REFORM COMMITTEE

collected ; it implies a detailed knowledge of facts about
their motion."*

The huge temples, called Ziggurats, ruins of which
have been found in Mesopotamia, are supposed to have
been dedicated to the planetary gods, each storey being
assigned to a particular god. It was the duty of temple
priests to keep the planets under observation, and
record their positions on the only writing material
available then viz* clay-tablets. Hundreds of thousands
such clay tablets have been discovered in the ruins of
Ziggurats, royal palaces and libraries, and patiently
interpreted by western scholars like Kugler.

the moon, and the planets, and compilation of tables
of positions, which afforded the basis on which modern
astronomy has been built up. In the large number of
ancient horoscopes which have been studied by
scholars, and in the astronomical tables compiled by
ancient and medieval scholars, we have a huge
amount of data on planets.
Pannekoek observes :

"The circumstance that made this possible for astro-
nomy was the occurrence of extremely simple and striking
periodicities in the celestial phenomena. What looked
irregular on occasional and superficial observing revealed

its regularity in a

Fig. 13— Ziggurat.

(Reproduced from Zinner's Gesckichte der Hternkunde)

At first, planetary astrology appear to have baen
confined to states, and kings or powerful officials
representing the state. But after the conquest of
Babylon by the Persian conqueror Cyrus (538 B.C.),
they appear to have been extended to private
individuals. Thus came into existence 'Horoscopic
Astrology', in which a chart is made of the 12 signs
of the zodiac with the position of the planets shown
therein, for the time of his birth, from which are
foretold the events of his life and career. We are
not interested in 'Horoscopic Astrology' at all, but
wish only to remark that but for the stimulus provided
by astrology, there would not have been that intense
activity during ancient and (from about 500 B.C.)
medieval times, for large scale observations of the sun,

continuous
SOUTH

abundance of data.

NORTH

* Pannekoek : The Origin of Astronomy— reprinted from the
; Monthly Notices of the Royal Astronomical Society, Vol III,
No. 4, 1951, pp. 351-52.

Fig. 14— Showing a horoscope cast in the European method.
The:£sign Aries, the first house or ascendant, is in the east.
The sign Capricornus, the 10th house, is on the meridian at the
time of birth and so is in the south. The planets occupying
the different signs are shown by the respective symbols.

CALENDARIG ASTEONOMY

197

Regularities were not sought for ; but regularities imposed
themselves, without giving surprise. They aroused certain
expectations. Expectation is the first unconscious form of
generalized knowledge, like all technical knowledge in daily
life growing out of practical experience. Then gradually the
expectation develops into prediction, an indication that the
rule, the regularity, has entered consciousness. In the
celestial phenomena the regularities appear as fixed periods,
after which the same aspects return. Knowledge of the
periods was the first form of astronomical theory". *

The astronomical knowledge which the Chaldean
astronomers bequeathed to the world are :

(1) Conception of the celestial equator and
racognition of the ecliptic as the sun's path.

(2) A number of relations between the synodic
and other periods of the moon and planets, vix.,

1 year = 12.36914 lunar months ;

modern value = 12.36827 lunar months.

Mean daily motion of the sun — 59' 9" ;
modern value = 59' 8'\3.

Mean daily motion of the moon -=13° 10' 35" ;
modern value = 13° 10' 35".0

Extreme values of the true motion of the moon :
15° 14' 35" to. IF 6' 35 .

According to modern determination these limits
are about 15° 23' to 11° 46'.

Length of the anomalistic month — 27.55555 days ;
modern value = 27.55455 days.

Or 9 anomalistic months = 248 days ;
modern value = 247.991 days.

Length of the synodic month = 29.530594 days ;
modern value = 29.530588 days.

223 synodic months = 242 draconitic months.

This gave rise to the Chaldean Saros cycle
of eclipses.

269 anomalistic months = 251 synodic months.
The length of the anomalistic month
deduced from this relation = 27.554569 days,
the modern value being .27.554550 days.

The Greek papyri gives longitudes of the moon for
dates 248 days apart. This period is based on the
Babylonian relation : 9 anomalistic months = 248 days.
After eleven such steps of 248 days, there is a big step
of 303 days in the ephemeris. The length of the
anomalistic month derived from these steps are as
follows.

*Pannekoek : The Origin of Astronomy, p. 352.

No. of anomalistic No. of Length of the

months days anomalistic month

derived

D 9 248 27.555,556 days

A 11 303 27.545,455

C-11D+ A... 110- 3031 27.554,545
Actual value = 27.554,550

It is not sure whether these figures were arrived at
by the Babylonians or by astronomers of other places.
But these and the more accurate approximation of the
moon's motion is found in the Paftca Siddhantika of
Varahamihira and is found used by Tamil astronomers.

In the Paftca Siddhantika the synodic revolutions of
planets are given, but they apparently differ much
from the actual figures. The figures are quoted in
col. (2) of the table No. 9 below. The actual periods of
the synodic revolutions in days are given in col. (3).

Tahle 9. — Synodic revolutions
of planets from Panca-SiddhnntikiL

Planet As given Actual Converted from

in P.S. (days) Col. (2)

(days)

(1) (2) (3) (4)

Mars 768f 779.936 779.944

Mercury 114A 115.878 115.870

Jupiter 393£ 398.884 398.868

Venus 575| 583.921 583.880

Saturn 372| 378.092 378.093

Dr. Thibaut in his Paftca Siddhantika could not
explain the figures in col. (2). It can be verified that
we can obtain the figures in col. (3) if we multiply the
corresponding figures in col. (2) by

365.2422 u ^ , 5.2422,
360 ° r by + - 360 >

The figures obtained by such multiplication are
shown in col. (4), which are found to be very close
to the fgures in col. (3). The figures in col. (2) can be
explained in another way, vi%., they are in degrees
representing the arc through which the sun moves
between two conjunctions. In other words, the
figures in col. (2), not being ordinary mean solar days,
are 'saura days* of Indian astronomy, a snxra day
being the time taken by the sun to move through one
degree by mean motion, or 360 saura days = 365.2422
mean solar days. This explanation has been found by
O. Neugebauer (ride his Exact Sciences in Antiquity).
Most of these data were known to Hipparchos and also
to Geminus, a Greek astronomer, who flourished about
70 B.C.

The "astronomical science'' as evolved by the
Chaldean astronomers, is seen to be in reality the by-

198

KEPOBT OF THE CALENDAR REFORM COMMITTEE

product of the huge amount of astrological nonsense,
a few pearls in a huge mass of dung, as Alberuni
observed nearly ten centuries ago. Let us see when
these "pearls" gradually crystallized out of the
dung-heap.

Two texts called 'Mul Afiri dated round about
700 B.C. have been discovered which contain summary
of the astronomical knowledge of the time. Here is
one of the pertinent passages from Neugebauer's
Exact Sciences in Antiquity (p. 96).

They *re undoubtedly based on older material. They
contain a summary of the astronomical knowledge of their
time. The first tablet is mostly concerned with the fixed
stars which are arranged in three "roads", the middle
one being an equatorial belt of about 30° width. The
second tablet concerns the planets, the moon, the seasons,
lengths of shadow, and related problems. These texts are
incompletely published and even the published parts are
full of difficulties in detail- So much, however, is clear :
we find here a discussion of elementary astronomical
concepts, still quite descriptive in character but on a purely
rational basis. The data on risings and settings, though
still in a rather schematic form, are our main basis for
the identification of the Babylonian constellations."

The passage indicates that the Chaldean astro-
nomers of this period could locate the north pole, and
had come to an idea of the celestial equator, and could

cuts the horizon at the east and west points as deter-
mined by the gnomon.

The Ecliptic :_From archaeological records, it is
generally held that a knowledge of the star-groups lying

Fig. 15— Two sculptured stones of ancient Babylon displaying the
Sun, the Moon, Venus and Scorpion— symbols of a primitive astro-
logical science which fathered the modern conception of astronomy.

close to the ecliptic was obtained in Babylon as early as

Rg. J&— Babylonian Boundary Btone showing Pythagorian numbers (Plimpton 322).
(Reproduced from Nengefaauer*B Enact Sciences in Antiquity)

trace it in the heavens. We do not know when
they came to the knowledge that tW celestial equator

1300 B.C for some of the ecliptic star-groups like the
Cancer, or Scorpion are found portrayed on boundary

CALENDABIC ASTRONOMY

199

stones which can be dated 1300 B.C. Neugebauer
and Sachs maintain that the ecliptic is first found
mentioned in a Babylonian text of 419 B.C., but its
use as a reference plane must have started much
earlier, probably before 550 B.C. But the steps by
which the knowledge of stars marking the ecliptic

Probably the first stage was to determine the
angular distance of heavenly bodies from some
'Normal Stars' as indicated by Sachs.* These normal
stars were stars either on the ecliptic, like Regulus,
Spica, or a Librae or some other stars close to it. Sachs
gives a list of 34 such normal stars. Probably the

Fig. 17— Babylonian Boundary stone showing lunar epheroeris
engraved on it (A. 3412 Rev.) {Exact Sciences in Antiquity)

was obtained, are not yet known with precision.
Only some guesses can be made.

The early astronomers probably observed that the
bright stars Regulus ( a Leonis ), Spica ( a VtrginisU
the conspicuous group Pleiades, and certain fainter
stars a Librae, a Scorvii were almost on tne suns
path. The ecliptic could be roughly constructed by
joining these stars.

'Regulus* or a Leonis was the 'Royal Star' in
Babylonian mythology. In Indian classics, it is known
as Magha (or the Great ) and the presiding deity is
Jndra, the most powerful Vedic god. It is almost
exactly on the ecliptic. Citra ( or a Virginis ) is 2° to
the south.

The First Point of Aries :— The first point of Aries
is the fiducial point from which all astronomical
measurements are made. But how was this point, or
any other cardinal point, say the first point of Cancer
( summer solstice ), the first point of Capricornus
( winter solstice ) and the first point of Libra, were
located on the circle of the ecliptic in early times ?

For rarely have the first point of Aries nor any
other of the cardinal points been occupied by prominent
stars during historical times. Even if for measurement,
the ancient astronomers used some kind of astrono-
mical instrument, say the armillary sphere, it would
be difficult for them to locate the first point of Aries
correct within a degree.

ecliptic positions of these normal stars were
determined after some effort by some method not yet
known, and then the positions of other heavenly

Fig. 18 — Armillary sphere.
(Reproduced from Kwyclopardia Britamniea).

bodies referred to the first point of Aries or the
beginning of a sign could be found. The early
observations are rough and no accuracy of less than a
degree is claimed by any classical scholar for them.

* A. Sachs, Babylonian Horoscopes, p. 53, Journal of Cuneiform
Studies, VoL VI, No. 2.

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REPORT OF THE CALENDAR REFORM COMMITTEE

Precession of Equinoxes :— But the first point of
Aries is not a fixed point on the ecliptic, though all
ancient astronomers belived it to be fixed once for all.
It moves steadily to the west at the rate of 50" per

Ptolemy's first point of Arias T is 4° to the west
of Hipparchcs's.

Clay tablet records have been obtained in
Mesopotamia which have been interpreted as represen-

--"-^

MAGNITUDES.

POSITIONS OF THE FIRST POINT OF
ARIES (T) IN DIFFERENT TIMES.

=. Vedic Times aboul 2300 B.C.

First

Second

Third

Fourth

Fifth

H=Hipparchoj

Pi.= Ptolemy

Si = SuryaSicfdhonfa

M= Modern

140 B.C.

150 A.a
185 AD.
500 A£.
570 A.D.
1S5Q A.D.

Fig. 19— The Zodiac through ages.

year. Astronomers of different ages must have given
measurements of stellar positions from observations
made either during their own times, or from
observations made by their predecessors, quite
unconscious of the fact that the reference point had
shifted. The result is that the positions of stars given
by different astronomers of antiquity do not tally, and
the positions given by the same astronomer are not always
consistent This is illustrated in Fig. 19 of the Zodiac.

Let us take Hipparchos's First point of Aries T as
our standard point.

ting two systems of Ephemeris known as Systems A and
B. System B indicates that the vernal point is Aries 8°.
This indicates that the observations were taken about
550 years before Ptolemy. This coincides approxi-
mately with the time of the Chaldean astronomer
Kidinnu, who observed at Borsippa near Babylon, and
is taken to be the author of the nineteen-year cycle.
System A uses Aries 10° as the vernal point ; the
author of this system might have flourished 120-150
years before Kidinnu, and may be identified with
Naburiannu, son of Balatu, who flourished about 490

CALENDABIC ASTRONOMY

201

B.C. Older still is the use of Aries 15° by Eudoxus of
Cnidus, the first Greek astronomer to start a geometri-
cal theory of planetary motion. This refers to
observations dating from about 810 B.C. These dates,
before they are accepted, should receive independent
verification.

The Use of Spherical Co-ordinates

The ancient astronomers were interested primarily
in the moon and the planets but later about 150 B.C.,
Hipparchos gives lists of fixed stars as well with their
positions.

It was clearly observed that though these planets
keep near the ecliptic, they deviate by small amounts*
sometimes to the north, sometimes to the south. In
the case of the moon, the maximum deviation amounts
to nearly 5° (inclination of the moon's orbit to the
ecliptic). In the case of planets, excepting in the case
of Mercury and Venus, the deviation was not large.

In the case of the moon, a knowledge of the moons
celestial latitude was necessary for prediction of
eclipses and therefore both the celestial longitude and
latitude used to be recorded by the Chaldean astro-
nomers of the Seleucidean period. In the case of planets,
only the celestial longitude appear to have been used.

The Chaldean astronomers were the first to frame
lunar and planetary ephemerides (i.e. calculation in
advance of lunar and planetary positions— the pre-
cursor of modern Nautical Almanacs and Ephemerides)
from about 500 B.C. But during these times, neither
the knowledge of the sphere nor of spherical or
plane trigonometry had developed. The Chaldeans
had only developed the ideas of angular measurement
which they expressed in degrees, minutes and seconds,
the whole circle being divided into 360° degrees.
Their methods, which have been elucidated by
Neugebauer, Sachs and others were arithemetical.
They took maximum and minimum values of astrono-
nomical quantities, and interpolated for an inter-
mediate period, assuming the change to be linear
(zigzag function, vide Neugebauer, Exact Sciences in
Antiquity, Chap. V, Babylonian Astronomy).

It was the Greeks who introduced geometrical
methods to deal with positions of heavenly bodies,
and made the next great advance in astronomy- But
they developed trigonometry only to a rudimentary
stage ( vide § 4-8). But they also used Babylonian
arithmetical methods alternately. Thus while Ptolemy
uses the trigonometric chord functions in his Syntaxis,
in the astrological text, called Teirabiblos, he uses
the Babylonian arithmetical methods.

Though the calendar, as we have seen, gave the
first stimulus for the cultivation of the astronomical

science, the use of astronomy for perfecting the
calender appears in the West to have come to a stop
after the Seleucidean era. For Rome conquered the
whole western Asia up to the Euphrates by about
80 A. D., and the Julian calendar replaced the
Babylonian luni-solar calendar, which have, however,
continued to currency probably in limited regions like
Syria, Arabia and Iraq amongst certain communities.
The Sassanid Persians also followed their own solar
calendars inherited from Acheminid times. But the
elements of the Chaldean luni-solar calendar have
been used in a limited way, for the Christian
ecclesiastic calendar for Christianity arose in Palestine
and Syria, and the most important event in Christ's
life, His crucifixion, is recorded in terms of the
luni-solar calendar prevalent in Palestine about the
first century A.D.

4.8 GREEK CONTRIBUTION TO ASTRONOMY

It has been considered necessary to give a short
account of Greek contributions to astronomy, because
there is a widespread vi>w that it was Greek astro-
nomy which formed the basis of calendar reform in
India which took place about 400 A.D. ( Siddhanta
Jyotisa calendar). Let us see how far this view is
correct. The Greeks themselves appear to have made
no use of astronomy for the reform of their own
calendars, as was done later in India. They cultivated
astronomy partly as pure science, partly as an
indispensable adjunct to astrology.

It is now well-known that Greek civilization had a
long past going back to at least 1500 B.C. The ^remains
of this civilization have been found in Crete (itfinoan),
and on the Greek mainland itself (Mycenean).
Inscriptions have been found in strange scripts (Linear

A, and B) which defied decipherment till 1952. We
have therefore as yet no knowledge of the calendar in
the Mycenean age of Greece (1400 B.C.— 1000 B.C.),
but probably they will now be forthcoming.

The Homeric poems 'Iliad' and 'Odyssey' written
about 900 B.C., as well as Hesiod writing about 700

B. C. show considerable acquaintance of stars and
constellations needed for sea-faring people, to find out
their orientation when out at sea.

From about 750 B.C., the Greek city-states began
to emerge ; they were engaged in maritime trade over
the whole Mediterranean basin. These activities
brought them into contact with many older nations
who had attained a high standard of civilization, e.g.,
the Egyptians, the nations of the Near East, vix., the
Lydians, the Phoenicians, and the Assyrians and
imbibed many elements of their civilization. The
older Greek scholars themselves admit that the Greeks

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REPORT OF THE CALENDAR REFORM COMMITTEE

borrowed their script* from the Phoenicians, their
coinage from the Lydians, their preliminary ideas of
geometry from the Egyptians and of astronomy from
the Chaldeans. But they enriched all these sciences
beyond measure by their own original thoughts
and contributions. As Plato (428-348 B.C.) proudly
remarks : "...whatever the Greeks acquire from foreigners,
is turned by them into something nobler"

Greek science goes no further back than Thales
of Miletus (624-548 B.C. ), who is reckoned to be the
first of the seven sages of Greece. Considerable
knowledge of astronomy and physics was ascribed to
him by later writers. He is supposed to have predicted
the occurrence of an almost total solar eclipse, which
occurred on May 28, 585 B.C., on the basis of his
knowledge of the Chaldean Saros. These stories are
now disbelieved by scholars well versed in Assynology,
for according to their finding, the Chaldeans them-
selves before 400 B.C., had no knowledge of the Saros
of 18 years 10J days used later to predict the eclipses,
but they used other methods with only partial success.
Thales might have used one of these methods, but not
certainly the Chaldean Saros. Considering the crude
state of Greek civilization in Thales' times, these
scholars think that it is a fairytale of modern times
that Thales knew anything about the Saros. Thales
lived in a coastal city of Asia Minor which had active
contact with the great civilizations of the Near East,
and probably much of the knowledge ascribed to him
were picked up from Babylon and Egypt.

The next figure in Greek astronomy is Anaximander,
( 610-545 B.C. ), likewise of Miletus a junior contem-
porary of Thales, who is said to have introduced the
use of the gnomon ( vide § 4"3). This may be conceded,
but this practice was derived most probably from the
Chaldeans, who used the gnomon from much earlier
times. Cleostratos ( 530 B.C. ) of Tenedos was cited
by later authors to have introduced the knowledge of
the zodiac, of the eight-year cycle of intercalations in
Greece, but probably he merely transmitted the
Babylonian knowledge and practice. Meton of Athens
is said to have introduced the nineteen-year cycle of
7 intercalary months in Athens in 432 B.C., but as
remarked earlier, its use in Greek calendars cannot
be dated before 342 B.C., though it was known in
Babylon from at least 383 B.C. The question of
priority of this discovery is still to be decided,
probably by fresh finds and interpretation of ancient

astronomical records.

"♦Ttl^pearT^t^Greekfl of Homeric poems used linear A
andB but about 900 B.C., they borrowed the simpler Phoenician
script' and adopted it to their use by the addition of vowels.
Thereby they forgot their old script and history, which became myth
and legend. The decipherment of Minoan Linear B has been
achieved in 1952 by Ventris and Chadwick.

We have besides philosophers of the Pythagorian
school ( 500-300 B. C. ), a religious brotherhood
which cultivated geometry, astronomy, physics and
mathematics. They are cited by later writers to
have propagated the view that the earth was
a sphere, and the planets were also spherical bodies
like the earth, but it is difficult to state when, and
on what grounds these theories were first propounded.

These were the periods of tutelage. Greek genius in
astronomy began to flower only after 400 B.C., and
was aided by a number of causes.

The first was the development of geometry as a
science by philosophers of the Pythagorean school
( 500-300 B. C. ), and other scholars, notably
Hippocrates of Chios ( 450-430 B.C. ), and Democritos
of Abdera ( 460-370 B.C.). A great impetus to both
plane and solid geometry was given by Plato ( 428-
348 B.C. ), famous philosopher and founder of a
school of studies and research known to the world as
the 'Academy*. Plato counted amongst his contem-
poraries and juniors several geometers of distinction.
viz.. Archytas of Tarentum (first half of fourth
century B.C. ), Theaitetus of Athens ( c. 380 B.C. ),
Eudoxus of Cnidos ( d. 355 B.C. ), and several others.
All tha geometrical knowledge developed by these and
other scholars was compiled, and rewritten into a
logical system with rich contributions of his own by
Euclid, who lived in the Museum of Alexandria
( 280 B.C. X And was bequeathed to the world in
thirteen ( or fifteen ) books known as the Elements
of Euclid, which have remained to this day the basis of
the teaching of elementary geometry. There is no
other book of science which have remained current
and authoritative for such a long stretch" of time, now
extending over two thousand years.

The second factor was political. During the sixth
and fifth centuries before Christ, the Greek savants
and scholars had indeed undertaken educational
journeys to the Near East in search of knowledge
—journeys which were made possible and safe under
the orderly regime of the Acheminid empire (Persian).
But it was the conquest of the Persian empire by
Alexander of Macedon in 330 B.C., which rendered
these contacts easier and more fruitful. The Greek
successor dynasties, viz., the Ptolemaic dynasty in
Egypt, and the Seleucid dynasty in Babylon and other
dynasties in Asia Minor were all great patrons of
learning and encouraged and maintained scholars ;
the former set up the famous Museum at Alexandria,
which was a research institution with a great library,
an observatory and other necessary equipment. It
attracted scholars from all parts of Greater Greece
and provided them with free board, lodge and a salary.
This place nurtured a number of great Greek geniuses :

CALBNDAEIC ASTBONOMY

203

Euclid, already mentioned; Eratosthenes who first
measured correctly the diameter of the earth and
was the founder of scientific chronology ; and others
whom we shall meet presently.

On the Asiatic side, under the centralized rule of
the Seleucids, the later Chaldean and Greek astrono-
mical efforts became very much intermingled. A
Chaldean priest, Berossus, who lived during the reign
of the second Seleucidean king Antiochos Soter
( 282-261 B.C. ), translated into Greek the standard
Chaldean works on astronomy and astrology. The
period from 340 B.C. to 150 A.D. may be called the
most flourishing period of astronomical studies in
antiquity. The Chaldeans figured prominently during
the earlier part of this period but their methods
were based on a primitive form of algebra and
arithmetic. According to Neugebauer, their contri-
butions in mathematics and astronomy were as good
as those of the contemporary Greeks who used
geometry, but they gradually faded into obscurity
on account of their infatuation with astrology ; and
the Greeks, though they were great believers in
astrology, freed themselves at least from astrolatry,
and cultivated astronomy as part of astrology, and
emerged as leaders in astronomical science.

The earliest Greek astronomer to use geometrical
ideas in astronomy is, if we leave aside the Pytha-
goreans, probably Eudoxus of Cnidos ( d. 355 B.C. ),
a junior contemporary, friend and pupil of Plato.
He made great original discoveries in geometry, and
Books V and VI of Euclid are ascribed to him. It
was probably his knowledge of geometry which led
him to make the first scientific attempt to give a
geometrical explanation for the irregular motions of
the sun, the moon, and the planets. Twenty-seven
spheres, all concentric to the earth were needed to
account for these motions. This theory had but a
short life, but it is remarkable as the first instance,
when heavenly bodies, connected with great gods,
were treated on a human level.

Eudoxus is supposed to be the inventor of
geometrical methods for determining the sizes and
distances of the sun and the moon, usually ascribed
to Aristarchus of Samos (ft. 280 B.C.), who is known to
have taught that the daily revolution of the celestial
sphere was due to the rotation of the earth round its
axis. He is also said to have first put forward the
heliocentric theory of the universe. Neither of these
theories was accepted by contemporary astronomers.
The world had to wait for the appearance of a Coper-
nicus (1473-1543), for the acceptance of these views.

Apollonius of Perga (born about 262 B.C.) known
more for his treatise on Conies, originated the theory

of epicycles, and eccentrics to account for planetary
motion. He was a junior contemporary of two
great figures : Eratosthenes already mentioned and
Archimedes of Syracuse (287-212 B.C.), a great
figure in mechanics, hydrostatics and other sciences,
but to astronomy, he is remembered as originator of
the idea of Planetarium— a revolving open sphere
with internal mechanisms with which he could imitate
the motions of the sun, the moon, and the five planets.

Archimedes is also credited with attempts for
finding out the actual distances of the planets from the
earth. We do not know whether this is correct or not,
but about this time, we find the planets arranged accord-
ing to the order of their distances from the earth :

Moon, Mercury, Venus, Sun, Mars, Jupiter, Saturn
or if we take the reverse order :

Saturn, Jupiter, Mars, Sun, Venus, Mercury, Moon.
This last order was taken up by astrology and formed
the basis of the seven-day week, which came into
vogue about the first century A.D.

The greatest name in Greek astronomy is
Hipparchos of Nicaea, in Bithynia who settled in the
island of Rhodes and had an observatory there
(ft. 161-127 B.C.J. He probably corresponded with the
savants at the Museum of Alexandria. Not much of
his writings have come down to us, except through
quotations and remarks by Claudius Ptolemy, the
famous Alexandrian astronomer who flourished three
centuries later. Sarton writes about Hipparchos :

"It is possible that all the Ptolemaic instruments, except
the mural quadant, had already been invented by him (e.g.
diopter, parallactic and meridian instruments). He was the
first Greek observer who divided the circles of his instru-
ments into 360 degrees. He constructed the first celestial
globe on record.

He used and probably invented the stereographic
projection. He made an immense number of astronomical
observations with amazing accuracy".

The principle of measurement of angles was
certainly derived from the Chaldeans. Hipparchos gave
a catalogue of 850 stars with their positions which
is reproduced in Ptolemy's Syntaxis. Vogt found
that of the 471 preserved numbers giving position,
64 are declinations, 67 are right ascensions, 340 are
in polar longitudes and latitudes, which reappear in
the Surya Siddhanta, six hundred years later.

It is suggested that after his discovery of precession
( vide § 4.9 ), Hipparchos probably used celestial longi-
tudes and latitudes. But these co-ordinates had been
already used by the Chaldeans at least a century earlier.

Hipparchos had probably some knowledge of plane
and spherical trigonometry necessary for the solution

C. B.-34

204

BBPOET OF THE CALENDAB KEFOBM COMMITTEE

of astronomical problems, e. g., finding out the time
of rise of zodiacal signs during the year, a problem
of great importance to horoscopic astrology. It is the
current opinion that he used the double chord,
illustrated below :

Chord (2 a)«2 R Sin a

Fig. 20

and gave a table of double-chords from 0° to 90°,
which was later improved by Ptolemy in his Syntaxis.
It is suggested by Neugebauer, that the 'Sine function
(Jy& in Hindu astronomy) was introduced 600 years
later by Xryabhata, and replaced the double chord.
The Hindu astronomers used Utkramajya which is the
ver sine function, 1 — cos a, but do not appear to have
used the cosine function as such. Neither the Greeks
nor the Hindus used the tangent, and the cotangent,
which were introduced by Arab astronomers about the
ninth century (al-Batt3M, 858-929 A.D.), and were
known in Latin in early days as Umbra Versa, and
Umbra Extensa ( extent of shadow ) respectively.
These are reminiscent of the practice of designating
the zenith distance Z of the sun by the length I of the
shadow of the gnomon, l = p tan Z, p being the height
of the gnomon.

Between Hipparchos and Claudius Ptolemy
(150 A.D.), who lived at the Alexandrian Museum
from 128 A.D. to 151 A.D., there is a gap of 300
years, which saw the phenomenal rise of horoscopic
astrology. There are, however, very few great names
in astronomy. Menelaos, a Greek astronomer who
lived in Rome about 98 A.D.> laid the foundation of
spherical trigonometry, but it was confined to a
transversal proposition from which Ptolemy deduced
solutions for only right angled spherical triangles,
of which either two sides or an angle and one
side are given. The Hindu astronomers likewise used
only solutions of right angled spherical triangles.
The discovery of general relations in spherical
triogonometry was the work of Arabic astronomers
(al-Battanl).

Claudius Ptolemy who worked at Alexandria
between 128-151 A.D., was, as Sarton says, a man of
the Euclidean type. Great equally as an astronomer,
mathematician, geographer, bhysicist, and chronologist,
his main work is the great mathematical and astro-
nomical treatise known in Greek as 'Syntaxis? , and in

Arabic translation as the Almagest. It has been long
supposed that it rendered all previous treatises in
astronomy obsolete, and remained a standard text,
which fertilized the brains of all ancient and medieval
astronomers, Greek, Jew, Arab, and European, till
the rise of the heliocentric theory of the universe
rendered it obsolete. This opinion appears to have
been rather exaggerated. Strangely enough, the
Syntaxis appears to have been quite unknown to Hindu
astronomers of the 5th century A.D.

Ptolemy's chief contribution to astronomy was his
elaborate theory of planetary motion and discovery of
a second inequality in the motion of the moon, now
called Evection. He gave a catalogue of 1028 stars
with their positions, most of which have been shown
to have been taken from Hipparchos by adding 3° to
the longitudes given by him. This represents the
shift of the first point of Aries since Hipparchos's
time according to Ptolemy's calculation. The actual
value is 4°.

Ptolemy wrote a treatise on astrology known as
the "Tetrabiblos" which long remained the Bible of
the astrologers.

After Ptolemy, there were no great figure in
astronomy except few commentators and workers of
mediocre ability like Theon of Alexandria (about
370 A.D.), who initiated the false theory of trepidation
of the equinoxes, and Paulus of Alexandria (fl. 378
A.D.) who wrote an astrological introduction. He is
supposed to have been the inspirer of the Indian
Siddhanta known as 'PauliM Sid&hania 7 {vide § 5'6 ),
but this hypothesis started by Alberuni has never
been proved. With the advent of Christianty, and
after murder of the learned Hypatia (415 A.D.). the
light' goes out of Greece.

The Greek contributions to astronomy are :

A geocentric theory of the universe, with the
planets in the order given on page 203.

The treatment of planets as spherical bodies
similar to the earth.

Geometrization of astronomy, development of
the concepts of the equator, the ecliptic and of
spherical co-ordinates (right ascension and declination,
celestial latitude and longitude), some elementary know-
ledge of plane and spherical trigometry to deal with
astronomical problems.

Knowledge of planetary orbits, and attempts to
explain them with the aid of epicyclic theories.

4.9 DISCOVERY OF THE PRECESSION OF
THE EQUINOXES

In the previous sections, we have stated how the
Chaldean and Greek astronomers started giving

CALENDARIC ASTRONOMY

205

positions of planets, and stars, with the point of
intersection of the ecliptic and the equator — the first
point of Aries — as the fiducial point. We shall now
relate how the discovery was made that this point is
not fixed in the heavens, but has a slow motion
along the ecliptic, to the west at the rate of ca. 50"
per year. The rate is very small* but as it is unidirec-
tional and cumulative, it is of immense importance
to astronomy, and incidentally is very damaging to
astrology.

When the sun, in course of its yearly journey
arrives at the first point of Aries, we have the vernal
equinox. The first point of Aries is therefore also
called the vernal point.

The position of the vernal point has rarely in the
course of history, been occupied by a prominent star,
but in India, as narrated in § 5*4, its nearness to star-
groups as well as the nearness r of other cardinal
points to star-groups have been noted from very early
times. Traditions of different epochs record different
stars as being near to the cardinal points. But
nobody app?ard to have drawn any conclusion from
these records {vide for details § 5'4 ).

In Babylon also, different sets of positions of
stars and planets record Aries 15 1 , Aries 10°, and
Aries 8° (the zero is of Ptolemy's) as being the vernal
point. But no Chaldean astronomer to our knowledge
appears to have drawn any conclusion from these data.

The first astronomer known to have drawn
attention to the precession of the equinoxes was
Hipparchos. He particularly mentions that the
distance of the bright star Spica (a Virginis or Citra)
has shifted by 2° from the autumnal equinoctial
point since the time of his predecessor Timocharis
who observed at Alexandria about 280 B.C. He
concluded that the autumnal point, and therefore also
the vernal point, was moving westward at the rate of
51J seconds per year.

It is not known whether Hipparchos considered
the motion as unidirectional. It was impossible for
him to say anything definite on this point, as
obeservations extending over centuries are required to
enable one to make a definite statement on this
point.

Though Hipparchos made, as time showed, one of
the greatest astronomical discoveries of all times,
which is all-invportant for the calendar, as well as for
astronomy, its great importance does not appear to
have been realized by either his contemporaries or
followers for thousands of years.

Let us, therefore, dwell a little on the consequences
of this discovery. Later and more accurate observa-
tions have shown that the rate is nearly 50" per year,

but is subject to variations which we may disregard at
this stage. The shift is accumulative and in 100 years
would amount to 1° 24'; and in about 26000 years the
first point will go completely round the ecliptic.
The period depends upon certain factors and is not
constant.

The tropical year, or the year which decides the
recurrence of seasons, is the time-interval for the
return of the sun in its orbit, starting from the year's
vernal equinoctial point to the next vernal equinoctial
point. If these points were fixed on the ecliptic, the
tropical year would be the same as the sidereal year,
which is the same as the time of revolution of the
earth in its orbit. But since the vernal equinoctial point
slips to the west, the sun has to travel 360° 0' 0"-50"
= 359° 59' 10" to arrive at the new vernal equi-
noctial point, hence the duration of the tropical year is
less than that of the sidereal year by about 20 minutes.
In exact terms :

duration of the sidereal year -365.25636 mean solar days

tropical „ =365.24220

at the present time.

Further Consequences of the Precession
of the Equinoxes

We may now consider some consequences of the
precession of the equinoxes.

Hipparchos appears first to have marked out the
beginning of the astronomical first point of Aries. It
started 8° west of the star a Arietis. Ptolemy had
found that it had shifted by his time by about 3°,
and gave the rate of precession as 36" per year. In
this, he was wrong, the true shift being about 4\
Ptolemy in his 'Uranometry' gives the starting point
of the sign of Aries as 6° to the west of (3 Arietis, and
the other constellations marked at intervals of 30°
may be marked out on the zodiac. The picture (Fig. 19)
gives the boundaries of the different signs according to
Hipparchos. The boundaries cf the signs of Ptolemy
would be 4° to the west of those of Hipparchos.

By the time of Ptolemy, (and probably much
earlier), a complex system of astrology had developed
which connected men's destiny in life with the
position of planets in the different signs at the time
of his birth (horoscopy). It was claimed that even
the fortunes of nations and countries could be
calculated in advance from planetary positions in the
signs. Though a few rational men like Seneca and
Cicero were as much sceptical about the claims
of astrology as the modern man, the general mass
became converted to its claims, even astronomers not
excepted. Even the great Ptolemy wrote a treatise
*The Tetrabiblos 3 exposing the principles of Astrology.

206

BBPOBT OF THE CALENDAR. BEFORM COMMITTEE

In fact, belief in astrology was one of the main
incentives for the observation of the positions of
heavenly bodies in ancient and medieval times which
were carried out by medieval astronomers with so
much zeal under the willing patronage of influential
persons.

The discovery of precession is very disconcerting
to astrologers, for in the astrological lore, the signs
are identified with certain fixed star-clusters ; whereas
precession tends to take them entirely out of these
star-clusters. Thus since Hipparchoss time, the shift
has been nearly 30 degrees, and what was the sign of
Pisces in Hipparchos's time has now become the sign
of Aries, and the astronomical sign of Aries has now
nothing to do with the Aries constellation.

This consequence must have been foreseen by the
followers of Ptolemy, and they probably started, more
on psychological than on scientific grounds, to find
out theories to mitigate the devastating influence of
precession on astrology. Astronomers immediately
following Ptolemy barely mentioned precession. It
was first referred to by Theon of Alexandria (ca. 370
A.D.) who invented the theory of Trepidation, i.e., he
said that the precessional motion was not unidirec-
tional, but oscillatory. He gave the amplitude of
oscillation as 8°. Probably this figure was suggested
by the fact that at Theon' s time the first point of
Aries had shifted by a little less than 8° from
Hipparchos s position, and Theon thought that it
would go back and save astrology.

Proclos the successor (410-485 A.D.), head of the

Platonic Academy at Athens, a very learned man and

one of the founders of Neoplatonism, denied the
existence of precession !

After the sixth century A.D„ the dark age set in
Europe and the mantle of scientific investigation fell
on the Hindus and the Arabs. Let us see how the
Arab astronomers regarded the precession.

Thabit ibn Qurra (826-901 A.D.), who flourished
at Baghdad under the early Abbasides, translated

Ptolemy's Almagest into Arabic ; he noted precession,
but upheld the theory of trepidation. But the other
great Arabic astronomers like al-Farghanl (861-
Baghdad), al-Battanl (858-Syria), Abd al-RahamSn
al-Sufl (903-986-Teheran) and Ibn Yunus (d. 1009—
Cairo), all noted precession and rejected the theory
of trepidation. In fact al-Battani gave the rate of
precession as 54" per year, which is far more correct
than the rate given by Ptolemy, vh., 36" per year.

But unfortunately, Europe recovering from the
slumbers of dark ages were more influenced by the
Spanish-Muslim astronomers al-Zarquali (L029-1087 of
Cordova), and al-Bitruji (ca 1150, living at Seville),
who upheld the theory of trepidation. As their
influence was considerable, they were largely
responsible for its diffusion among the Muslim, Jewish
and Christian astronomers, so much so that Johann
Werner (1522) and Copernicus himself (1543) were still
accepting it ; Tycho Brahe and Kepler had doubts
concerning the continuity and regularity of the
precession, but they finally rejected the trepidation.
The theory of trepidation was completely given up in
Europe after 1687, when Newton gave a physical
explanation of it from dynamics and the law of
gravitation. This is given in appendix (4- A), for the
benefit of Indian astrologers and almanac-makers who
still believe in the theory of trepidation and oppose
reform of the wrong calendar they are using for
centuries.

Sarton from whose writings much of this account
has been compiled, writes* :

"The persistence of the false theory of trepidation is
difi&cult to understand. At the very beginning of our era,
the time span of the observations was still too small to
measure the precession with precision and without
ambiguity, but as the centuries passed there could not
remain any ambiguity. Between the stellar observations
registered in the Almagest and those that could be made by
Copernicus, almost fifteen centuries had elapsed, and the
difference of longitudes would amount to 21°"

* Sarton, A Eisiory of Science, p. 446.

APPENDIX 4-A

Newton's Explanation of the Precession
of the Equinoxes

In view of the prevailing confusion in the minds of
Indian almanac makers regarding precession of the equinoxes,
a short sketch of the physical explanation of the phenomenon
originally given first by Newton is given here in the
hope that those amongst Indian calendar makers who
believe in science, may be persuaded to give up their belief
in the theory of trepidation and be converted to the
sayana reckoning advocated in these pages. This
explanation will be found in any standard book on Dynamics
or Dynamical Astronomy, e.g., in Webster's Dynamics.

We have now to regard the earth as a material sphere,
spinning rapidly round its axes, which is inclined at an
angle of ? — w to the plane of the ecliptic, where « = obliquity
of the ecliptic to the equator.

The earth is kept in its orbit by the gravitational pull of
the sun, which is situated at one of the foci of the earth's orbit
which is an ellipse. Dynamics shows that the plane of the
ecliptic is almost invariant, i.e., does not change with time,
except a very small oscillation due to attraction of other
planets on the earth. What is then precession due to ?

This is explained by means of the following figure.

Fig. 21 — Showing the precession of the equinoxes.

In the above figure (No. 21), C is the pole of the ecliptic
EL'L. Let T ± midway between E and L be the firsj;
point of Aries for year 1. Then the celestial pole is P 1(
and the celestial equator is E X T X Q X . Due to precession of
the equinoxes, the first point of Aries is slowly moving in
the backward direction 1/ T r E along the ecliptic. If T ±
ahtfts to T , in year % the celestial pole shifts to P 2
*long the small circle P* P* P B ...where CP = obliquity of

the ecliptic. The celestial equator assumes a new position
E 2 T 2 Q* in year 2.

The celestial pole P therefore goes round the pole of the
ecliptic C, and it makes a complete cycle in a period of about
26000 years as shown in fig. 22.

At present (1950 A. D.), the celestial pole is 58' from
Polaris (a Ursce Minoris) which is a star of the second
magnitude. CP, i.e., the line joining the pole of the ecliptic
G to the celestial pole P continues to approach the Polaris
up to 2105 A. D., when the pole would be only 30' away from
the star and will then begin to recede from it.

Polaris Q f R ota tion

Former
Pole Star

4600 B.a

d Cygni

14 800 A.D.
^aLyrce

Fig. 22— Showing the precessional path of the celestial
4 pole among the stars,

(Taken from Astronomy by Russell & others)

It will be seen that the celestial pole has not been
marked with a prominent star for most part of this period
of 26000 years. About 2700 B. C, the second magnitude
star a Draconis was the pole-star, as was probably known
to the ancient Egyptians, the Chinese and the Rg-Vedic
Hindus. Conscious human history hardly goes beyond this
period. The prominent stars which will become pole stars
in future are :

7 Cephei 4500 A.D.

a Cephei... 7500 A.D.

8 Cygni 11200 A.D.

a Lyrse (Vega) . . .13600 A.D.

The last *is a first magnitude star, the brightest in the
northern heavens and can be easily picked up with the
naked eye.

207

208

EEPORT OF THE CALENDAR REFORM COMMITTED

The phenomenon of precession of the equinoxes tells us
that in addition to rotation, the earth has another motion,
viz., a slow conical motion of its axis round the pole of
the ecliptic which causes the equinoxes to move bakward.
The phenomenon can be visualized by reference to the
motion of tops played by boys (Fig. 23).

It is a matter of common experience with those who
have played with tops that when the top is thrown spinning
on the earth, the axis round which the top is spinning very
often is not vertical, but is oblique ; and it is also having a
slow motion in a circle round the vertical as shown
in fig, 23. This last motion is precessional motion. The
top may be likened to the earth, and the vertical direction
of gravity, corresponds to the pole of the ecliptic. The

Fig. 23— Motion of a top.
The spinning top, which is likened to the earth , causes
precessional motion of its axis.

top would have fallen but for its spin. When it slows down,
the top falls down ; the precessional motion of the top is
due to the pull exerted by the gravity.

Now turning to the earth, we see that as a first
approximation, we may take it as a point of mass concentrated
at the centre, and then deduce its orbit as is done in
classical planetary theory. This would have been all right,
if the earth were a homogeneous sphere. But the earth is not
a sphere, but a spheroid, having its polar axis shorter than
the equatorial axis by 43 kms. ( — 27 miles). There is an
equatorial bulge of matter. The pull due to the sun, is now
equivalent to a force in the ecliptic passing through the centre
of the "earth defining the orbital motion, plus a couple, which
tends to turn the equator of the earth into the plane of the
ecliptic. It is this couple which produces precessional motion.

For details of calculation the reader may refer to a book
on Rigid Dynamics, say A.G. Webster, Dynamics, pp. 298-302,

We mention only the results here :

If ^ be the angle of precession, i.e., the angle P ± CP a in
fig. 21. we have due to the sun s attraction

. 3ym V C — A a ( . sin 2 ^

where :

y = gravitational constant = 6.67 X 10- 8 c. g. s. units ;

C = moment of inertia of the earth round the polar axis ;
A = moment of inertia of the earth round an equatorial axis ;

w = obliquity of the ecliptic ~ 23° 26' 45" ;
m = mass of the sun = 1.99 X 10 33 gms ;
r ^distance of the earth from the sun = 1.497 X 10 13 cms ;

~— tide-raising term ;
r 3

1 = longitude of the sun ;

n — angular velocity of the earth ;

£ — angular rotational speed of the earth in radians.

If the earth were a homogeneous sphere, C would be — A r
and — 0. But taking the polar radius c~a (1- «), where
€ = ellipticity of the earth, it can be shown that for the earth,
in which concentric layers are taken to be homogeneous
(G-A) 1 / , *

But actually — — — is the mechanical ellipticity of the earth,

the value of which has been found by observation as —

304

Substituting the values as given above in the expression
d\pft Sym C - A 07 \
lU Mr* • "C" «» "(!-«»*)

we get the progressive part of the solar precession
-2-46X10- 12 .

This is in radians per second of time. To convert it to
seconds of arc per year, we have to multiply the expression
by 2.063x10 s X3.156X10 7 .

2.063 X 10 5 being the number of seconds of angle in
a radian, and 3.156 X 10 7 the number of seconds of
time in the year.
We have therefore the rate of solar precession

= 16."0 per year.
We have now to calculate the action of the moon which,
in spite of its much smaller mass, exerts a far larger
perturbing force as the lunar distance is much smaller. In

fact the tide raising force (^r~) * or * ne raoon * s m ^Te than

double that of the sun. This makes the rate of lunar
precession = 34". 4 per year.

But there is another complication. The moon's orbit is
not coincident with he sun's path (ecliptic) but is inclined
at an average angle of 5° 9', the extreme values being 5° 19'
and 4° 59'. Further the points of intersection of the moon's
orbit with the ecliptic travel round the ecliptic in a period of
18.6 years. The pole of the moon's orbit M therefore moves
round the pole of the ecliptic C as shown in fig. 24 in a
period of 18,6 years. The lunar precessional angle \p», has
therefore to be defined from the instantaneous position of Jf.

Combination of the two precessional motions*

The two precessions can be combined as in fig. 24. Here
C, M are the poles of the ecliptic and of the moon's orbit.
P is the celestial pole. The solar precession can be

CALENDARIC ASTRONOMY

209

represented by the vector ^, along the line PS perpendicular
to CP, but the lunar precession is represented by the vector
PJR, which goes up and down as M goes round G in a

_,- : -JF R

Fig. 24 — Combination of two precessional motions.

complete cycle of 18.6 years (period of moons node).
Therefore the motion is equivalent to

= Cos MPG... parallel to PS.

$ n =^ m gin MPG... perpendicular to PS.

This causes certain irregularities in the precessional
motion and also in the annual variation of the obliquity of

the ecliptic, which would otherwise have been uniform.
These periodic (period = 18*6 years) variations are known
as Nutation.

Annual Rate of Precessional Motion

The solar and lunar precessions amount to 50. "37 per
tropical year, with a very small centurial variation. After
making necessary corrections for the slight motion of the
plane of the ecliptic due to attraction of planets, the annual
rate of general precession in longitude is obtained as
follows : —

Rate of precession = 50."2564 +0."0222 T per trop. year,

where T— Tropical centuries after 1900 A.D.

The nutation in longitude may amount to ±17. "2
according to different positions of the lunar node, but its
effect on the annual rate of precession does not exceed ±5. 8,
so that the actual precession rate per year may vary
between 44. "5 to 56. "0.

The average rate of annual precession is not constant,
it is very slowly increasing. The annual rate for certain
epochs along with the period taken by the equinoxes to move
through 1°, are however stated below : —

Hate of precession

2000 B.C. 49."391

49.835

1900 A.D. 50.256

2000 A.D. 50.279

No. of years per degree

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72.24
71.63
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CHAPTER V

Indian Calendar

5.1 THE PERIODS IN INDIAN HISTORY

The time-periods in Indian history necessary for
our purpose are shown in the Chronological Table.

The earliest civilization so far discovered in India
is the Harappa-Mohenjo-Daro civilization (sometimes
also called the Indus-Valley civilization) named after
the two ancient buried cities of Harappa in the
Punjab and Mohenjo-Daro in Sind. They were first
brought to light by the late R.D. Baner jee, Superinten-
dent of the Western Circle of Archaeology of India in
1924. It has now been ascertained that this
civilization extended right upto Rupar on the Sutlej
in the east and to the Narmada valley in the south.
This civilization was certainly contemporaneous with
the Mesopotamian civilizations of about 2500 B.C.,
nearly 500 years before the city of Babylon had risen
to supremacy amongst the cities of Sumer and Akkad ;
and with the first dynastic civilization of Egypt. How
far back it projected into the time-scale is not yet
known, but certainly many thousand years back.

From the material records of the Indus-valley
civilization, it is obvious that the Harappa-Mohenjo-
Daro people had attained to as high a standard of
civilization, if not higher, as the contemporary people
of Iraq and Egypt. But the script has not yet been deci-
phered ; it is therefore difficult to give a chronological
history, but it is not so difficult to make a study of the
attainments of this civilization in arts and sciences ;
they could build well planned cities, used a drainage
system superior to that of contemporary Egypt or Iraq,
used copper and bronze, and had evidently evloved a
highly complex social organization.

All civilized communities have been found to have
evolved accurate systems of weights and measures and
some kind of calendar for the regulation of social
life. We have some evidences of the use of standard
weights and measures in the Indus valley.

But had they evolved a calendar ? The presump-
tion is that they must have, but nothing has yet been
discoverd amongst the artefacts left by these people so
far recovered by the Archaeological Survey which
throws light on the calendar, or the system of time-
measurement they used.

It is held on quite sound grounds that the Harappa-
Mohenjodaro people were succeeded in the Punjab
and in the valley of the now lost Sarasvati river by
the Aryan people who were either autochthonous or
more probably came through Afghanistan in single or

successive streams between 2500 B.C. and 1500 B.C.
Others would go further back in time-scale from
certain astronomical evidences.

Few, almost none of the material records or
artefacts of the early Aryans except some potteries
tentatively ascribed to them, have so far been
discovered. Almost the whole of our knowledge about
them are derived from the hymns of the Rg-Vedas
which were composed by priestly families amongst
them in an archaic form of Sanskrit (Vedic Sanskrit),
in honour of the gods they worshipped ; in these
hymns are found occasional references to the sun, the
moon, certain stars, and to months and seasons. Some
think that there are also references to planets, i.e., the
Vedic Aryans could distinguish between fixed stars
and planets, but this is doubtful. From certain
references which we discuss in § 5.2, we may conclude
that they used an empirical luni-solar calendar.
Probably this was used till 1300 B.C. We do not
come across sufficient material records until we
come to the time of Asoka about 270 B.C. .

What was the calendar during the period
1330 B.C. — 250 B.C. ? The Yajur-Veda, the Brahmanas,
the Upani$ads and other post Rg-Vedic literature, and
the early Buddhistic literature contain occasional
astronomical references, from which the nature of
the calender used for ceremonical and other purposes
can be inferred. The interpretation of the texts is
neither easy, nor unambiguous. The latter part of
this period has been called by S. B. Dlksit, our pioneer
in calendar research, as the Vedahga Jyotisa period.
This is discussed in § 5.4.

The Vedanga Jyotisa calendar appears to have
been almost completely free from foreign influence,
though this point of view has been contested. The
Persian conqueror Darius conquered Afghanistan, and
Gandhar, about 518 B.C. ; this region appears to have
continued under the Achemenids for nearly two
centuries. The Achemenids used a solar calendar
probably adopted from Egypt in contrast to the
luni-solar calendar of India, but this does not appear to
have disturbed the indigenous luni-solar calendancal
system.

The Vedahga Jyotisa period, which as we shall
show, was continued by Indian dynasts up to the time
of the Satavahanas (200 A.D.), was succeeded by the
Siddhania Jyotisa period, but the first record of this
period is available only about 400 A.D. The transi-

212

INDIAN CALENDAB

213

tional period from 100 A.D. to 400 A.D. is one of the
darkest periods in Indian chronology. Due to
successive invasions by Macedonian and Bactrian
Greeks ( Tavanas ), Parthians ( Pallavas X Sakas and
Kusanas, the period from 300 B.C. to 200 A.D. is one
of large foreign contacts which profoundly modified
Indian life in arts, sciences, sculpture and state-craft.
But the history of this period was entirely forgotten
and is being recovered bit by bit from inscriptions,
foreign references, and from artefacts recovered in
excavations of the sites occupied by invaders of this
period. Let us give a bird's eye view of the* history of
this period, imperfect as it is, so that the reader may
follow without strain our account of the transition of
the Vedanga Jyoti$a calendar to Siddhantic calendar.

In 323 B.C., Alexander of Macedon raided the
Punjab, but this incident by itself had no such
profound influence on Indian life as is generally made
out. Its influence was rather indirect. In India, it
gave rise to a great national movement of unification
under Candragupta and-Canakya. In the former
empire of Darius, it gave rise to a number of Greek
states which became the focus of radiation of Greek
culture throughout the East. The most important
were Egypt under the rule of the Ptolemies, with
capital at Alexandria, and the Near East under the
Seleucids with capital at Babylon, which was
succeeded a few years later by Seleucia a few miles
distant from later Baghdad. In 306 B.C., Candragupta
and Seleucus faced each other, but the Greek army
was rolled back to the borders of modern Iran, and
almost the whole of modern Afghanistan except
Bactria (modern Balkh) constituting the four satrapies
of the old Persian empire were ceded to India. They
continued to be politically and culturally parts of
India till the tenth century A.D.

The Mauryas kept out the Greeks till 186 B.C.,
when on the break-up of their empire, the Greek
settlers in Bactria who had revolted from their
overlords, the Seleucids, began to make inroads ipto
India. There -were two rival Greek houses, the
earlier, the Euthydemids who under Demetrius and
Menander (175 B.C.) took possession of the Punjab
and Sind between 180 B.C. to 150 B.C. and threatened
even Pataliputra but were rolled back beyond the
Jamuna by the Sungas ; the line of Eukratidas who
ousted Demetrius and his line from Bactria and
Afghanistan proper about 160 B.C., reigned in
Afghanistan up to 50 B.C. But there rose about
226 B.C., a great barrier between the Eastern Greeks
(Bactrians and Indian Greeks) and the Western
Greeks in the shape of the Parthian empire (248 B.C.),
which became very powerful under Mithradates I

(175 — 150 B.C.), who controlled the whole of Iran and
wrested Bactria from the line of Eukratidas in 138 B.C.

But inspite of these political happenings, Greek
remained the language of culture throughout the
whole Near East, from Asia Minor to North- Western
India. The Parthians since 128 B.C. called themselves
Thilhellens* or lover of Greek culture and used Greek
on their coins, and the Graeco-Chaldean method of
date-recording on their inscriptions. But about 140
B.C., a new power was on the move, vix., the Sakas
from Central Asia ; they began to emerge as a ruling
race from about 138 B.C. In 129 B.C. they attacked
Bactria, and by 123 B.C. they wrested it completely
out of the Parthian empire, after defeating and killing
on the battlefield two successive Parthian emperors,
vix., Phraates II (128 B.C.) and Artabanus I (123 B.C.).

The early Sakas appear from their coins to have
been under the spell of Greek civilization, and
used Greek as a language of culture and put motifs
taken from Greek mythology on their coins. Pressed
by the next Parthian emperor, Mithradates II
(123—90 B.C.), they poured by 80 B.C., into the
whole of what is modern Afghanistan, except the
Kabul valley, which the Greeks held for sometime.
Their new territory became known as 'Sakasthan*
comprising modern Afghanistan and parts of N.W.
India. From Afghanistan, they poured in successive
streams to Malwa, Guzrat, Taxila about 70 B.C., and
to Mathura, somewhat later and had put an end to
the numerous Greek principalities in the Punjab.
Their further progress was barred by the Satavahanas
in the South, and numerous small kingdoms which
arose in the Gangetic valley on the break-up of the
Sunga and Kanva empires (45 A.D.). After 50 A.D.,
the Sakas of the North were supplanted by the Kusanas
belonging to a kindred race, and speaking the Saka
language ; they ruled Northern India from their
capitals at Peshawar and Mathura up to at least 170
A.D. Contemporaneously with them, were the Saka
Satrap houses of Ujjain, who started ruling from
about first century of the Christian era.

A chart of these historical incidents is attached
for the sake of elucidation as they are necessary
for the comprehension of the extent and amount of
Greek culture, which was propagated into India, not
so much through the Greeks directly, but as it appears
now, indirectly through the early Sakas and their
successors, the Kusanas.

It now appears very probable that it was during
the regime of the Saka and Kusana ruler s (100 B.C.-
200 A.D.) that a knowledge of the Graeco-Chaldean
astronomy, which had developed in the Grecian world
after 300 B.C., and ended with the astronomer

214

KBPORT OF THE CALENDAR REFORM COMMITTEE

Ptolemy (150 A.D.), and in the Near East under the
Seleucids (300 B.C. to 100 A.D.), penetrated into
India, being brought by astronomers belonging to the
Saka countries, who later were absorbed into Indian
society as &akadvipi or Scythian Brahmins. The
borrowings appear to be more from Seleucid Babylon
than from the west. The knowledge of Graeco-
Chaldean astronomy was the basis on which the
calendar prescribed by the Surija Siddhanta and other
Siddhantas were built up. It completely replaced the
former Vedanga Jyotisa calendar and by about 400 A.D,
when the Vedanga Jyotisa calendar had completely
disappeared from all parts of India.

From 400 A.D. to 1200 A.D., almost the whole of
India used calendars based on Siddhanta Jyotisa for
date-recording. All Indian astronomers used the
Saka era for purposes of accurate calculations, but its
use for date-recording by kings and writers was
generally confined to parts of the South. In general,
the Indian dynasties used eras of their own, or regnal
years, though the annual calendar was compiled
according to rules laid down either in the Surya
Siddhanta, the Arya Siddhanta or the Brahma
Siddhanta, These did not much differ in essentials.

When India since 1200 A.D. fell under Islamic
domination, the rulers introduced the lunar Hejira
calendar for civil and administrative purposes as well.
Indian calendars were retained only in isolated
localities where Hindus happened to maintain their
ndependence, or used only for religious purposes.
The emperor Akber in 1584 tried to suppress the
Hejira calendar for administrative purposes by the
Tarikh-llahi, a modified version of the solar calendar
of Iran, but this fell in disuse from about 1630. Since
the advent of British rule in 1757, the Gregorian
calendar has been used for civil and administrative
purposes, which is still being continued.

We have attempted to give below short accounts
of calendars in use in different epochs of history.

5.2 CALENDAR IN THE MG-VEDIC AGE
( —1200 B.C. )

The Vedic Literature : The knowledge of the calen-
dar in this age can be obtained only from the Vedic
literature which consists however of different strata,
greatly differing in age. According to the great
orientalist Max MUller four periods each presupposing
the preceding can be distinguished. They are

(a) The Chandas and Mantras composing the
Safnhiias or collections of hymns, prayers, incantations,
benedictions, sacrificial formulas, and litanies

comprising the four Vedas : The Rk t Sama, Yajus
and Atharva.

(b) The Brdhmanas which are prose texts contai-
ning theological matter, particularly observations on
sacrifices and their mystical significances ; attached
to the Brahmanas, but reckoned also as independent
works are the Aranyakas or Upanisads containing
meditations of forest hermits and ascetics on* God. the
world, arid mankind. These treatises are attached to
each of the individual Vedas.

Sutra or aphorism literature which grew as results of

attempts to understand the Vedas in their various

aspects, and sometimes to develop the ideas contained

in the Vedas. According to the orthodox view, there

are six Veddngas as follows :
*

(1) Siksd : or phonetics ; texts explaining how
the Vedic literature proper is to be pronounced, and
memorized.

(2) Kalpa : or ritualistic literature, of which
four types are known : Srauta Sutras dealing with
sacrifices ; Qrhya Sutras dealing with domestic duties
of a householder ; Dharrna Sutras dealing with
religious and social laws ; Sftlva Sutras dealing with
the construction of sacrificial altars.

(3) Vyakarana : or Grammar, e. g. 9 Panini's famous
Astddhyayii which once fpr all fixed up the Sanskrit
language. The As\adhyayi is however the culmination
of attempts by large number of older authors, whose
works were rendered obsolete by Pacini' masterpiece.

(4) Nirukla or Etymology: explanation of the Vedic
words ascribed to one Yaska, who lived before Panini.

(5) Chandas— Metrics ascribed to Pingala.

(6) Jyotisa— Astronomy: the Rg- Jyotisa is ascribed
to one Lagadha, of whom nothing is known.

Only the sixth Vedanga or Jyotisa interests* us,
though there are occasional references to the calendar
in all Satra literatures.

Age of the Vedic Literature *

The above gives the 'Philologists' stratification of
the age of the Vedic literature. About the actual
age of each strata, there is great divergence of opinion,
though it is admitted that the oldest in point of age
are the Safnhitcis. then come the Brahrnanas and

* Much of the substance-matter of this section is taken from
Winternitz's A History of Indian Literature Vol. I, published by the
University of Calcutta. Chap. I, on Vedic literature.

INDIAN CALENDAR

215

Upanisads, next the Sutras or the Ved&figas. Of
the four Vedas, the Rg- Vedas are by common consent
taken to be the earliest in age and as Winternitz
remarks, though all subsequent Indian literature refers
to the Rg-Vedas, they presuppose nothing extant.

Max Mtiller made a rough assignment of age to
the different strata as follows on the assumption that
the BrSThmanic and Upanisadic literature predated
the rise of Buddhism, and that the Sutra literature
which may be synchronous with the Buddhistic
literature may be dated 600 B.C. to 200 B.C. Working
backwards he assigned the Brahmanic literature to
600 B.C. to 800 B.C., the interval 800 B.C. to 1000 B.C.
as the period in which the collections of hymns were
arranged, and 1000 B,C. to 1200 B.C, as the period of
the beginning of Vedic poetry. He always regarded
these periods as terminus ad quern, and in his Gifford
Lectures on Physical Religion in 1889, he expressly
states "that we connot hope to fix' a terminus a quo.
Whether the Vedic hymns were composed 1000, 1200,
2000 or 3000 years B.C., no power on earth will ever
determine. *

It is not correct therefore to say, as some people
say, that Max Mtiller had proved that 1200-1000 B.C.
is the date of the Rg- Vedas. t

Other authorities, Schrader, Tilak, Jacobi, and
P. C. Sengupta have found much older age for Rg- Vedic
Indians : in fact, even as early as 4000 B.C., for some
incidents described in the Rg-Vedas.* But their
arguments, being based on interpretations of vague
passages assumed to refer to astronomical phenomena
have not commanded general recognition.

Let us first look at the strata within the Rg-Veda
itself. The Rg-Vedas are divided into 10 Mandalas
( lit circles ) or books. Of these, the 2nd to the 8th
books are ascribed to certain priestly families, eg,
the 2nd book is ascribed to Gritsamadas, the 3rd to
the Vi§v&mitras, etc. These are agreed to be the
oldest parts of the Vedas.

The ninth book is devoted to Soma which is an
intoxicating drink pressed out of a plant. The drink
was dear to the Aryans and is also mystically
identified with the Moon.

* For details about Vedic antiquity, see Ancient Indian
Chronology by P. C. Sengupta.

+ It appears that Max Midler lias been a bit. dogmatic in his
opinion. Shortly after his death the names of the Vedie gods, Indi a,
Varufta, Mitra and the Nasatyas in their Kg- Vedic forms were
discovered in the Hittitc clay tablets discovered at Hoghnz Knei in
Aeia Minor. They have been assigned to about 145U B.C. More
evidences about the Vedic Aryans were discovered in the excavations in
the SarasvatI valley now being undertaken by the Arehaelogical Dept.
of the Govt, of India. Further, fresh evidences are expected also in
the archaelogical work undertaken in Afghanistan, Iran and Central
Asia.

The first and the tenth books are miscellaneous
collections ascribed to different authors. They are
taken to be the latest in age.

The Rg-Vedas consist of 1028 hymns, containing
over 40,000 lines of verses.

The Vedas are regarded as '&rutis' or 4 revealed
knowledge preserved by hearing." According to
savants, they were the outpourings of the heart and
mind, of ancient priestly leaders, to their gods which
were mostly forces of nature, intermingled very often
with secular matter. Priestly families were trained
to memorize the texts and pass them on to succeding
generations in ways which guaranteed their transmi-
ssion without error or alteration of the text.
Savants are almost unanimous in their opinion that
the Rg-Vedic texts which were composed in an archaic
form of Sanskrit, which was not completly understood
even in 500 B.C„ have come to us without change.
The orthodox Indian view that they are revealed
knowledge is of course not shared by scholars, both
eastern and western, who point out that very often
in the text of the Vedas themselves and in Anukramatyis
or introductions to texts, the authors of each hymn
are mentioned by name and family.

To which locality are the Vedas to be ascribed ?

As regards locality, they are certainly to be
ascribed to parts of Afghanistan, east of the Hindukush
and the Punjab. The rivers of the Punjab, the
Indus and its tributaries on both sides and the now
lost SarasvatI are frequently mentioned, the Ganges
only once in a later text. The authors call themselves
Aryas or Aryans, in contrast to the Dasas or Dasyus
who were alien to them, and with whom they came
in frequent clash. The Dasyus are now taken to be
partly Indus valley people, partly aboriginals.

The Rg-Vedas describe a highly complex society
of priests, warriors, merchants and artisans, and slaves
but the rigid caste system had not yet developed.
There are also references to cities, but no artefacts
except some pottery, have yet been discovered which
can be referred to the Rg-Vedic Aryans.

The Rg-Vedic Aryans, it appears, were con-
temporaneous (if not older) with the great civilizations
of Mesopotamia, both Sumerian, and later Accadian,
and according to one view, some of the royal families
of Asia Minor, were probably 'Vedic, Aryans'. It is
therefore quite probable that they had attained as
high a stage of civilization as that of Egypt of the
Pyramid builders (2700 BC), or of Sumer and Accad
under Sargon I.

Let us see what information we can gather about
the calendar which they must have used, for no
civilized community can be without a calendar.

216

Further, the whole life of Vedic Aryans was centred
round sacrifices to their great gods ; and sacrifices had
to be carefully timed with respect to seasons and
moon's phases. In fact, some sacrifices were year-long,
as Dr. Martin Haug. the great Vedic scholar remarks
in his introduction (p. 46) to Ailareya Brahmana
(affiliated to the Rg-Veda).

"The Sattras [or sacrifices] which lasted for one year,
were nothing but an imitation of the sun's yearly course.
They were divided into two distinct parts, • each of six
months of thirty days each ; in the midst of both was the
Vwvan, i.e., equator, or central day, cutting the whole
Sattra into two halves*.

This refers to somewhat later times than the
Rg-Veda, but even during these early times, the
sacrificial cult was fully developed. Let us see what
references we get about the calendar from the
Rg-Vedic times.

Calendarie and Astronomical References
in the Rig-Vedas

These are few, and interspersed along with other
matter This is not to be wondered at, for the hymns
are addressed chiefly to the gods, Agni (sacrificial
fire) Indra (the national warrior god), etc., and other
references are only incidental. The direct references
are found only in Books 1 and 10 which are later in
age than the family books.

Let us give the texts of a few hymns and their

translations in English.

Rg-Veda. 1.164.11

Dvadasararh nahi tajjaraya varvarti cakram

paridyamvtasya

A putra agne mithunaso atra sapta satani

vimsatisca tasthuh.

Translation : The wheel (or time) having twelve
spokes revolve round the heavens, but it does not
wear out. Oh Agni! 720 pairs of sons nde this
(wheel).

Here the year is likened to a wheel, having 12
spokes (or months) ; the 720 pairs of sons are 360'-days
and nights.

The interpretation commonly accepted is that the
year was taken to consist of 360 days divided into 12
months, and the night and the day (following or
preceding) constituted a couple.

Ifg-Veda. 1.164.48.

Dvadasa pradhayaseakramekam trini nabhyani

ka u tacciketa

Tasmin tsakam trisata na sankavo'rpitah

sa?tirna calacalasah.

REPORT OF THE CALENDAR REFORM COMMITTEE

Translation : Twelve spoke-boards : One wheel :
three navels. Who understands these ? In these there
are 360 sankus (rods) put in like pegs which do not
get loosened".

The year is compared to a revolving wheel, whose
circumference is divided into 12 parts (twelve months).
They are grouped into three navels (seasons).

Here also we have a year of 360 days, divided into-
12 months, four months constituting a season, as we
find in the oldest inscriptions.

If the interpretation of the last passage is correct,
we have the earliest reference to the later caturmasy*
system, or division of the year into three seasons each
of four months.

It appears from these passages that Vedic Aryans,
had once a year of 360 days as ancient Egyptians also-
had but they discovered later that this was not the
correct value either for 12 lunar months, or for a
seasonal year. For the following reference shows that
they used also a thirteenth month.

Jig-Veda, 1.25.8

Veda maso dhvtavrato dvadasa prajavatah

vedaya upajayate.

Translation: Dhftavrata ( Vamna) knows the
twelve months : (and) the animals created during that
period ; (and) he knows (the intercalary month>
which is created (near the twelve months).

This passage makes it clear that the calendar
was luni-solar. But how was the adjustment made ?

A hymn in the Gg-Veda first noted by Tilak
comes to our help.

Ilg-Veda, 4.33.7

Dvadasa dyun yadagohyasya tithye ranannrbhabat

sasantab-

Suksetrakrnvannanayam ta sindhun dhanvatistha

nnosadhir nimnamapalj.

Translation: When the #bh™ sleeping for
twelve days have made themselves comfortable as
guests of the unconcealable (sun), they bring the fields
in good order and direct the rivers. The plants ^grow
in wildernesses, and lowland is spread with water \

According to Tilak, the Ifbhus are the genii of
seasons. They are said to enjoy the hospitality of
the sun for twelve days in the above verse. This
passage, according to Tilak means the adjustment of
the solar year with the lunar (i.e., 366—354 = 12
days).*

* r/. Ancient Indian Chronology, Chapter VI.

INDIAN CALENDAR

217

Another hymn from Atharva Veda (4.11.11) states
that : 'PrajSpati, the lord of yearly sacrifices after
finishing one year's sacrifice, prepared himself for the
next year's sacrifice*.

The sacrificial literature of India still preserves
the memory of these days by ordaining that a person
wishing to perform a yearly sacrifice should devote
12 days (dvadasaha) before its commencement to the
preparatory rites.

Did the Rg-Vedic Aryans have any knowledge
of the lunar zodiac, or designate the days by the lunar
mansions, as we find widely prevalent during later
times ?

There is no explicit reference to this point, but
words which are now used to denote the lunar
mansions are found in several verses of the Rg-
Vedas, e.g.,

Citra" ( rt Virginia) is mentioned in RV. 4-51-2
Magna" (a Leonis ) is mentioned in RV. 10-85-13

but in these passages the meaning of these words is

not very clear.

The following references are more explicit.

J?g- Veda, 5. 54. 13
Yusma dattrasya Maruto vicetaso ray all syama
rathyo vayasvatah na yo yucchati tisyo yatha
divo'sme raranta Marutah sahasrinam.
Translation : You wise Maruts, we would like to
be disposer of the wealth conferred by you on us it
should not deviate (from us) as Tisya does not deviate
from the heavens.

Here one is tempted to identify the word 'Tisya' with
the lunar asterism of that name, vi% t , Pusya (S Cancri).
The following reference is more explicit.

Rg- Veda, 10. 85. 13

Suryaya vahatuh pragat savita yamavasrjat
Aghaau hanyante gavo'rjunyori paryuhyate.

Translation ; The (dowry) of cows which was
given by Savita (Sun) had already gone ahead of Surya.
On the Agha-day, the cattle were slain (acc. to Sayana
had departed), on the two Arjuni- days, she was led
to the bridegroom's house.

This passage occurs in the famous bridal hymn,
where the Sun god (Savitr) gives away his daughter
Surya to Soma (Moon) in marriage. It says that on the
Agha~day the cows, given as bridal dowry are, driven
away ; on the two Arjunl-d&y% the bride goes to the
bridegroom's house.

This hymn is repeated in the Atharva Safnhitd
as follows :

Atharva Safnhita, 14.1.13
Suryaya vahatmi pragat savita yam avasrjat
Maghasu hanyante gavah phalgumsu vyuhyate.

Translation : The first line is identical. In the
second line, the only change is Magha for Agha, and
Phalgunl for Arjunz. In the lunar zodiac, Magha
stands for lunar asterism No. 10, of which the chief star
is a Leonis. The two Phalgunl stars, Uttara Phalgunl
(No.12) and Purva Phalgunl (No. 11) stand for Leonis
and 8 Leonis.

This verse shows that the custom of designating
the day (it means day and night) by the lunar asterism
in which the moon is found in the night, which is
found widely in vogue in later times, and is used even
to-day for religious purposes, was in use at the time
when this hymn was written. The practice therefore
dates earlier than 1200 B.C. at least.

Longer periods of Time : The Yuga

'Yuga is a very common word used in Indian
literature of all times to denote an integral number of
years when certain astronomical events recur. It
exactly corresponds to the Chaldean word 'Saros'
which has gone into international vocabulary. In
later Indian literature we have Yugas of all kinds : the
five yearly yuga, sixty yearly yuga, and Mahayugas of
4*32 xlO 6 years. Was any Yuga, known in Rg-Vedic
times ?

There is evidence that some kind of a short period
yuga, probably the five yearly yuga of later times, in
which the moon's phases roughly recur, and which
was the chief theme of the Vedanga Jyotisa was
known in Rg-Vedic times as the following quotation
shows :

Rg-Safnhita, 1.158.6
Dirghatama mamateyo jujurvan dasame yuge
apamartham yatinam Brahma bhavati sarathhS.
Translation : Dirghatama the son of Mamata
having grown old in the tenth yuga became the
charioter of the karma which leads to semi-result.

The most rational explanation of the word yuga
here is probably the five yearly yuga of Vedanga
Jyotisa for it is rational to expect that a man becomes
old after he attains the 50th year. But there have
been other explanations.

The Seasons and the Year

The most commonly used word for year in the
Indian literature is Varsa or Vatsara. The word
4 Versa is very similar to Varsa, the rainy season, and
is probably derived from it. But curiously enough,
this word is not found in Rg-Vedas. But the words
&arad (Autumn), Hemanta (early Winter) etc., ate very
often found to denote Reasons' and sometimes years,

218

REPORT OF THE CALENDAR REFORM COMMITTEE

just as in English we very often say l A young lady of
eighteen summers'.

Summary : The above passages show that the
Rg-Vedic Aryans, who must be placed at least before
1200 B.C., had a luni-solar calendar, and used
intercalary months. We do not have, however, their
names for the 12 months, and there is no clue to find
out how the intercalary month which is mentioned
at one place was introduced. It appears ihat they
denoted individual days by the naksaira i.e., by the
lunar asterism in which the moon is found at the
night, and hence it is permissible to deduce that they
used the lunar zodiac for describing the motion of
the moon. There is no mention of the tithi ^or the
lunar day) widely used in Indian calendars, in the
Rg-Vedas. The solar year was probably taken to
consist of 366 days, of which 12 were dropped for
luni-solar adjustment.

5 3 CALENDARIC REFERENCES IN THE
YAJUR VEDIC LITERATURE

The Atharva Veda consisting mostly of magic
incantations also contain calendaric references, but
we shall make only occasional use of them, as the text
of this Veda has not probably come to us in unadul-
terated form, for the Atharva Veda was not regarded
as holy as the Rg-Veda.

Of the two other Vedas, the Sama-Vedas contain no
new matter than what is contained in the Rg-Veda.
But there are copious calendaric reference in the
Yajurveda for obvious reasons, which are clearly
brought out in the following extracts from Winternitz's
introductry remarks to Yajurvedic studies (p. 158-159) :

"The two Sarhhitas [Rk and Atharva] which have so far
been discussed have in common the fact that they were not
compiled for special liturgical purposes. Although most
of the hymns of the rJg-Veda could be, and actually were
used for sacrificial purposes, and although the songs and
spells of the Atharvaveda were almost throughout employed
for ritualistic and magic purposes, yet the collection and
agrrangement of the hymns in these Samhitas have nothing
to do with the various liturgical and ritualistic purposes.
The hymns were collected for their own sake and arranged
and placed, in both these collections, with regard to their
supposed authors or the singer- schools to which they
belonged, partly also according to their contents and still
more their external form-number of verses and such like.
They are as we may say, collections of songs which pursue a
literary object.

It is quite different with the Samhitas of the two other
Vedaa, the Samaveda and the Yajurveda. In these collections
we find the songa, verses, and benedictions arranged

according to their practical purposes, in exactly the order in
which they were used at the sacrifice. These are, in fact,
nothing more than prayer-books and song-books for the
practical use of certain sacrificial priests — not indeed
written books, but texts, which existed only in the heads of
teachers and priests and were preserved by means of oral
teaching and learning in the priests' schools.*

The Yajurvedas were compiled for the use of the
Adhvaryu priest " Executor of the Sacrifice" who performs all
the sacrificial acts, and at the same time uttering prose
prayers and sacrificial formulae (Yajus). They are the
liturgical Samhitas, and prayer books of the priests.

Winternitz gives reasons to believe that the
Sarhhitas of the Black Yajurveda school are older than
those of the White school.

Even such a conservative thinker as Berriedale
Keith gives 600 B.C. as the terminus ad quern for the
verses of the Yajurveda Samhita". As we shall see,
there are references which point to a much earlier
origin.

The Yajur-Veda gives the names of twelve months,
and the names of the lunar mansions with their
presiding deities, and talks of the sun's northernly and
southernly motion. We do not give the texts here,
but only Dr. Berriedale Keith's translation.

Taittiriya Safnhita, 4.4.11

(a) (Ye are) Madhu and Madhava, the months

of Spring.

(b) (Ye are) Sukra and Suci, the months of Summer.

of Rain.

(d) (Ye are) Isa and Drja, the months of Autumn.

(e) (Ye are) Sahas and Sahasya, the months

of (Early) Winter (Hemanla).

(f) (Ye are) Tapas and Tapasya, the months of

cool season.

* There are two schools of the Yajurveda Samhita each with
a number of recensions as shown below :

1. The Black Yajurveda School, with the following recensions :

fa) TheKathaka

(b) The Kapisthala-Katha-Samhita, which is preserved only
in a few fragments of manuscript.

(d) The Taittiriya-Samhita, also called "Apastamba-
Samhita" after the Apastamba-School, one of the chief
schools in which this text was taught— shortly called T. S.

These four recensions are closely inter-related, and are designated
as belonging to the "Black Yajurveda*'. Differing from them is the
White Yajurveda which is known as 6ukla Yajurveda.

2. The Vajasaneyi-Samhita shortly called V. S. which takes its
name from Yajfiavalkya Vajasaneya, the chief teacher of this Veda.
Of this Vajasaneyi-Samhita there are two recensions, that of the
Kanva and that of the Mfidhyandina-Bchool, which however differ-
very little from each other.

INDIAN CALENDAR

219

The month-names which are- given here and
repeated in many other verses of the Yajur-Veda
have been interpreted by all authorities to be tropical.
Further this is probably the earliest mention of month-
names in Indian literature ; these names are no longer
in use, and have been replaced by lunar month-names
{Caitra, Vai&akha, etc,) which are, however, found at a
later stage.

Madhu and Madhava have been taken in later
literature to correspond to the time-period when the
sun moves from -30° to 30° along the ecliptic, and
so on for the other months. But we have no reason
to believe that the Yajurvedic priests had developed
such a fine mathematical sense of seasonal definition.
But it is almost certain that they must have developed
some method of observing the cardinal points of the
sun's yearly -course, viz., the two solstices and the
equinoxes. From these observations, they must have
counted that the number of days in a year was 366 in
round numbers.

The Yajur-Veda speaks in many places of the
UttarViyana, the northernly course of the sun from
winter solstice to summer solstice and the Daksinayana
or the southernly course from summer solstice to
winter solstice and the Visuvan, or the equinoctial
point. The ayanas or courses must have received
their designation from daily notings of sunrise on the
eastern horizon. The year-long observation of shadows
cast by a gnomon, of which we have evidences, may
have formed an alternative method for fixing up the
solstitial days, and the cardinal points on the horizon,
(vide Appendix 5-C), where some passages from the
Aitareya Brahmaiia attached to the Rg-Veda are
stated in favour of the view that the cardinal points
were observed by means of the gnomon.

Once they learnt to anticipate the cardinal days,
determination of the month-beginnings marking seasons
would not be difficult. The Madhu-month (the first
month of spring) would begin 30 or 31 days before the
vernal equinox day or 61 days after the winter solstice
day, and the Madhava month on the day after the
equinoctial day and so on. Average length of 30£
days would be given to each month, or 30 and

31 days to the two months forming a season.

The Nakshatras

One of the peculiar features of the Indian
calendars is the use of the Naksatras as explained in
§ 41. Evidences have been given that the custom
started from Rg-Vedic times. But we come across a
full list of Naksatras only in the Yajurveda with
names of presiding deities as given in Table No. 10
( p. 220 ), taken from Dlksit's Bharatiya Jyotifastra.

There are several points to be noticed in this list,,
which may.be compared with the list given on p. 210.

First, the naksatras start with Kfttikas which all
authorities identify with the conspicuous group
Pleiades. What is the significance of this ?

At the present times, the naksatras start with
AMni, of which the junction star is a or Arietis.
This custom, Asvinyadi, was introduced in Siddhanta
Jyotisa time ( 500 A.D. ), when the astronomical first
point of Aries was near the end of the Revatt
naksatra ( ( Pisdum ), or the beginning of ASvini.
We do not enter into the controversy about the exact
location of this point by the Siddhanta astronomers,
which is fully discussed in Appendix 5-B. At present,
the astronomical first point had shifted by as much as
19° from £ Piscium, but the orthodox Indian calendar
makers do not admit in the continued precession of the
equinoxes, and still count the naksatras from Asvini.

In all older literatures, on the other hand, including
the great epic Mahabhdrata, whose composition or
compilation may be dated about 400 B.C., the first
naksatra is Kfttikd. It therefore stands to reason to
assume that at one time, when the naksatra enumeration
started, the Pleiades were close to the astronomical
first point of Aries, or rose near the true east. This
is implied in the following verse which S. B. Dlksit
picked out of the j&atapatha Brahmana :

&atapatha Brahmana, 2.1.2.

Ekarh dve trini catvariti va anyani
naksatranyathaita eva bhfiyistha yat krtfcika....
Eta ha vai pracyai diso na cyavante
sarvani ha va anyani nalisatrani
pracyai disascyavante.

Translation : — Other naksatras have one, two,
three or four ( stars ) only ; these Kfttikas have many
( stars ).. .They do not deviate from the east; all
other naksatras deviate from the east*

The names as given in this list are somewhat
different from those now adopted, which have come
into vogue since 500 A.D.; for example, we have :

No. 6 Tisya for Pusya

No. 16 Rohini for Jyestha

( There are thus two Rohinls, No. 2, and No. 16

No. 17 Vicrtau for Mala

No. 20 Srona for Sravana

No. 21 Sravistha for Dhanistha

No. 23 Prosthapada for Bhadrapada

No. 26 Asvajuya for Asvini

No. 27 ApabharanI for Bharanl

The more important question is whether the lunar
mansions denote definite clusters of stars, or the
naksatra-di visions of later times, amounting t6 13° 20'
or 800' minutes ? This point has been discussed in 3 4*1.

C. E.-36

220

EEPOBT OF THE CALENDAK BEFOBM COMMITTEE
Table 10.

Names of Nakshatras in the Yajurveda with their Presiding Deities

No,

2.
3.

o.
6.
7.
8.
9.

10.

11.
12.
13.

14.
15.
16.

17.

18.

19.

20.
21.

22
23.

Name of
Naksatra

Presiding
Deity

Number*
( Grammatical)

Bohini
Mrgasirsa

Invaka
Ardra
Bahil
Puttarvasu
Tisya
Airesa
Magha
Phalguni

Purva Phalguni
Phalgun f

Uttara Phalguni
Hasta
Citra
Svati

Nis^ya
Visakha
Anuradha
Bohini

Jyestha
Vioftau

Mulabarhani, Mula
Asadha

Purvasadha
Asadha

Uttarasadha
Abhijit
$rona
$ravistha
Satabhisak
Prosthapada

24. Prosthapada

25.
26.
27.

Bevati

Asvayuja

Apabharani

Principal
Star

Agni

7] Tauri

a Tauri

Soma

\ Orionis

Rudra

a Orionis

)»

Aditi

j8 Geminorum

Brhaspati

8 Cancri

Sarpa

€ Hydrae

Pifr

i ILL

a Leonis

Aryama

S Leonis

Bhaga

(3 Leonis

Savita

8 Oorvi

Tndvn. Tvasta

a Virginis

Vayu

a Bootis

Indragni

a Librae

Mitra

S Scorpii

Indra

a Scorpii

Pitr

X Scorpii

, Nirrti, Prajapati

a
D

A pah

S Sagittarii

Visvedeva

a Sagittarii

Brahma

a Lyrae

Visnu

a Aquilae

Yasu

£ Delphini

Indra, Varuna

X Aquarii

Ajaekapad

a Pegasi

Ahirbudhniya

7 Pegasi

Pusa

f Piscium

Asvin

/? Arietis

Yama

41 Arietis

Longitude
(1950'0)

59° 17' 39"
69 5 25-
83 31

88 3 22

29
23

112 31

128 1

131 38 59

149 8 1

160 36 52

170 55 23

192 45 23

203 8 37

203 32 8

224 23 7

241 52 23

249 3 51

263 53 14

273 52 55

281 41 11

284 36 54

301 4 16

315 38 38

340 52 38

352 47 19

8 27 32

19 10 40

33 16 18

47 30 19

Latitude

+ 4° 2' 46"

- 5 28 14

- 13 22 32

- 16 1 59

+ 6 40 51

+ 4 32

- 11
+

6 25
27 48

+ 14 19 58

+ 12 16 13

- 12 11 31

- 2 3 4
+ 30 46 3

+ 20' 19

- 1 58 49

- 4 33 50

- 13 46 56

- 6 27 58

- 3 26 36

+ 61 44 7

+ 29 18 18

+ 31 55 21

- 23 8
+ 19 24 25

+ 12 35 55

- 12 52
+ 8 29 7
+ 10 ~ 26 48

* S= Singular ; D =

The Lunar Month-Names

The solar month -names given earlier have not
gone into general currency. The month-names
generally used are of lunar origin as given in § 5-7.
These names are first found in the Taittirtya Safnhita
7.4.8, and in many other places of the Yajur-Veda
literature, but in a somewhat different form. We
quote parts of the passage.

Dual ; P = Plural.

Taittirtya Safnhita, 7.4.8.
Sarhvatsarasya yat phalguni purnamaso mukhata
eva sarhvatsaramarabhya diksante tasyai kaiva
nirya-yat sammedhye visuvant sampadyate
Citra purnamaso dikseran mukharh va etat samvatsarasya
yat citra purnamaso mukhata eva. . .
Translation .—One should get consecrated on the
■ Phalguni full-moon day because Phalgima full moon
is the "mouth" of the year. Hence, ( such people ) are

INDIAN CALENDAR

221

taken as consecrated from the very beginning of the
year. But such people have to accept one 'nirya'
(draw back), viz., that the 'Visuvan' occurs in
the cloudly season ( sammedhya ). Hence, one should
consecrate on the Citra full-moon day. The Citra full
moon month is the *mouth J of the year.

From these passages, we learn that the lunar month
came gradually. The ancient Indians reckoned by
the paksa or the fortnight, and distinguished the
closing full moon day of the pak$a by the naksatra
where the moon was full. Thus Phalguni Paurnamasi
is that full moon when the moon gets full near the
Uttara Phalguni star ( (3 Leonis \ one of the lunar
mansions. Caitri Paurnamasi is that full moon, when
the moon gets full near the Citra star ( a Virginis ),
which is the 14th lunar mansion. Later, as the months
were always full-moon ending, the word paurnamasi
was dropped, and, e.g., the first part of Caitra- Paurna-
masi, i.e., Caitra became the lunar month-name. The
above passage says that the Phalguna Paurnamasi
was regarded as the last day of the year and less
frequently the Caitra Paurnamasi. This system still
continues, and the first lunar month Caitra of the lunar
year begins on the day after Phalguni Paurnamasi.

There are twenty-seven naksatras and so only 12
can be selected for lunar month-names.

The twelve names which we have got are :

Caitra from Citra (No. 14)

Vaisakha „ Visakha ( „ 16)

Jyai§tha „ Jyestha ( „ 18)

Asa<}ha „ Asacjha ( „ 20 & 21 )

Sravana „ Sravana ( „ 22 )

Bhadra „ Bhadrapada ( „ 25 & 26 )

Asvina „ Asvini ( „ 1 )

Kartika „ Krttika ( „ 3 )

Margaslrsa „ Mrgasiras ( „ 5 )

Pausa „ Pusya ( „ 8 )

Magna „ Magha („ 10)

Phalguna „ Phalguni ( „ 11 & 12)

Of course, full moon takes place by turn in all
the naksatras. But only 12 at approximately equal
intervals could be selected. But we have too Rauhinya
paurnamasi etc. the paksa when the moon becomes
full near Rohini, or Aldebaran ( lunar mansion No. 4).
But Rauhinya was not selected for the name of a
lunar month, because it was too near Krttika- Paurna-
masi.

Tithi

'Tithi' or 'Lunar Day' is a very important concep-
ition in Hindu astronomy, for holidays are always dated
by the tithi. According to Siddhantic definition, a iiihi

is completed when the moon is ahead of the sun by
12°, or integral multiples of 12° ( vide § 57).

Thus the first tithi ( Pratipada, lit. when the moon
is regenerated ) in the waxing half starts when the
moon is in conjunction with the sun, and ends when
she has gone ahead of the sun by 12°, when the
second tithi of the waxing moon begins. The tithis
are numbered ordinally from 1 to 15, the end of the
fifteenth tithi being full-moon. Then begins the
tithis of the waning moon, numbered from 1 to 15,
the end of the 15th tithi being the new-moon. There
are thirty tithis in a lunar month, and though the
average duration is less than a solar day, being 23,62
hours, the length of individual tithis may vary from
26.8 to 20.0 hours., on account of irregularity in the
moon's motion.

This is the definition of the tithi given in
Siddhdntas or scientific astronomy which started about
400 A. D. But this presupposes knowledge of measure-
ment of angles, and precise scientific observation, of
which we find no trace in the Vedic literature. What
was then the origin of this system ?

We have no reference to tithi in the Rg-Veda.
The first reference is found in Yajurvedic literature,
and the Brahmanas. The Taittiiiya Safnhitd talks of
the pa%cadasi tithi, which shows that the lunar paksa
was divided into 15 tithis, counted by ordinal numbers
from 1 to 15 for each paksa. But what was the time-
period meant by a tithi ? The Aitareya Brahmana
attached to the Rg-Veda gives the following definition
of the tithi.

Aitareya Brahmana, 32.10
Yam paryastamiyad abhyudiyaditi sa tithih.
The tithi is that time-period about which the
moon sets or rises.

This has been interpreted by Prof. P. C. Sengupta
as follows :

During the waxing moon ( sukla paksa ), the tithi
was reckoned from moon-set to moon-set ; and during
the waning moon ( kfsna paksa ), the tithi was
reckoned from moon-rise to moon-rise. The tithis
were thus of unequal length, as shown by Prof. P. C.
Sengupta in Table No. 11 on page 222.

5.4 THE VEDANGA JYOTISHA CALENDAR

The history of the Indian calendar from the end
of the Yajurveda period to the beginning of the
Siddhanta Jyotisa period is very imperfectly known
though there are plenty of calendaric references
in the Brahmanas, Sutras, and the epic Mahahharata
and various literature. On time-scale, it extends from

222

REPORT OF THE CALENDAR REFORM COMMITTEE

Table 11.
Duration of Vedic Tithi

English
Date

(1936 A.D.)

Ending of Vedic Tithi

Modern
Tithi

Oct.

Amavasya

Pratipad

Dvi tiya

i ft

TrHvn

C^.a 4-11 v^Vl 1
wcu U Lll till 1

Pq T"l/"»a TYlT

Afl+QTYl 1

Navami

OK
Jib

Dasami

Ekadasi

art

Dvadasi

oo
28

TrayodasI

Caturdasi

Oil

Purnima

Pratipad &

Dvitiya

Nov.

Trtiya

Caturthi

Pari cam I

Sasthi

Saptami

Astami

Navami

Dasami

Ekadasi

Dvadasi

Trayodasi

Caturdasi

Amavasya

Nov.

Pratipad

Event

Moonset or Sunset

Moonset

Time of Event

Moonset

Moonrise or
Sunset

Moonrise

Moonrise
Sunrise
Sunset
Moonset

(L. M.

T.-

Duration of
Vedic Tithi

18 18

19 18

20 20

21 23

22 23

23 21

24 14

25 7

25 58

26 47

27 37

28 27

29 17

30 14

17 15

25
25
25
25

25 3

24 40

24 45

24 50

24 53

24 55

24 57

24 58

24 59

11 33

24 56

24 58

24 53

24 51

24 49

24 50

24 57

11 1

24 45

Vedic Elapsed
Tithi No.

1
2
3
4
5
6
7
8
9
10
11
12
13
14

16
17
18
19
20
21
22
23
24
25
26
27
28
29
1

Note : — The Vedic tithi ends
when the moon remains invisible,
tithis are of more than 24 hours'

at moonset in the light half and at moonrise in the dark half. Near amavasya
the ending is at sunset. There are 29 or 30 such tithis in a lunar month, and all
duration except amavasya and purnima which are of about 12 hours' duration.

an unknown antiquity, which is set by some at 1300
B.C. to 300 A.D.

The VeddTiga Jyotisa is generally assigned to this
period. It may be said to be a sort of collection of
short aphorisms giving mathematical rules for fixing
the calendar in advance, and is known in three
versions: the Rg-Jyotisa consisting of 36 verses,
attached to the Rg-Veda and ascribed to one Lagadha

as mentioned earlier, the Yajus Jyotisa attached to
the Yajurveda and consisting of 43 verses, and there
is a text ascribed to one Somakara, a commentator of
unknown age of the Vedas. The dffferent texts
contain about the same matter, but the verses are
haphazardly arranged showing that the original texts
have not come down to us in an unadulterated form.
The number of independent verses in all the versions

INDIAN CALENDAE

223

is not more than 49, and some of the verses have
not been interpreted.

There are several other calendarical treatises which
can be assigned to this period. The Surya Prajnapli,
a Jaina astronomical work, the Jyothakaranda, and
the Kdlalokapralcasa.

A short account of the calendaric rules followed
in these treatises is given in Varahamihira's Paftca
Siddhantika, Chap. XII, where the rules are collected
as <% Paitdmaha Siddhanta" or Astronomical Calendar
according to Grandfather Brahma, the Creator, in
Hindu mythology. That shows the high antiquity of
the rules. Varahamihira, as well as Brahmagupta
describe the rules as very "inaccurate" {Duravibhrastau,
furthest from truth in Varahamihira's language) though
they pay a formal courtesy to the supposed authors.
But such has been the case with calendars of all
ancient nations, including the Babylonians at this
period and a critical account of the Vedaiiga Jyotisa
is important from the historical point of view.

It may be remarked here that there are minor
differences between Vedaiiga Jyotisa, the Jain systems,
and the Paitamaha Siddhanta, which appear to be
the latest of this group. The older treatises have a
year of 366 days, while the Paitamaha Siddhanta has
a year of 365*3569 days (Dlksit).

There is an extensive literature on Vedaiiga Jyotisa
^hich has been studied by Dr. G. Thibaut, S. B. Dlksit,
;S. K. Pillai, and Dr. R. Shama Sastry, amongst others.
We here give an account of the calendar according
to the Paitamaha Siddhanta.

Summary of the Contents

"Five years constitute a Yuga or Saros of the sun
and the moon.

The yuga comprises 1830 savana days (civil days)
and 1860 tithis (lunar days).

In the yuga, there are 62 lunar months and 60 solar
months. So two months are omitted as intercalary
months, in a period of 5 years.

The number of omitted tithis in the period
is 30.

There are 67 naksatra-months (sidereal months) in
the yuga. The moon passes through 67x27 = 1809
naksatras within this period.

The yuga begins at winter solstice with the sun,
and the moon together at the Bham-siha asterism
(< or j3 Delphini)"

These are the main points from which the five
yearly calendar can be constructed.

The Vedaiiga Jyotisa further describes measure-
ments of the subdivisions of the day by means of the
clepsydra, as well as by gnomon- shadows.

One particular feature is the assumption that the
ratio of the length of.ifche day to that of the night on
the summer solstice day^rs as 3 : 2.

Let us now examine these points critically.

We observe that all the mathematical rules point
out only to mean motions of the sun and the moon, i.e ,
the periods of the sun and the moon were obtained by
counting the number of savana days in a large number
of years and months, and dividing the number by the
number of periods (year or month). No evidence is
found of the systematic cfay to day observations of
the sun and the moon. Only the lunar zodiac was
used for describing the positions of the sun and the
moon, which appears to have been divided into 27
equal parts or naksatras ; in other words the naksatras
no longer denoted star-clusters but equal divisions of
the lunar belt.

There is no mention of the zodiac or twelve signs
of the zodiac, or of week days, or of planetary motion.

Let us now look critically into the rules.
5 solar years = 365.2422 x 5 = 1826.2110 days ;

62 synodic months = 29 .53059 x 62 = 1830.8965 days ;

67 sidereal months = 27.32166x67 -1830.5512 days.

Therefore, regarded as a measure for luni-solar
adjustment, the error is 4.685 days in a period of 5
years, i.e., if we started a yuga with the sun and the
moon together on the winter solstice day, the
beginning of the next yuga (6th year) would occur 4.685
days later than the winter solstice and in 5 to 6 yugas
the discrepancy would amount to a month or half
season. This cannot escape notice, and therefore
there must have been some way of bringing back the
yuga to the winter solstice day. Otherwise the calendar
becomes useless. But how could it have been
done ?

This is a matter for conjecture and several
hypotheses have been proposed. According to S. B.
Dlksit, we should have in 95 years :

according to the F. J.,f x 95 = 38 intercalary months,
while actually we have, T \ x 95 = 35 intercalary months.

So the Verfanga Jyotisa rules introduce 3 more
intercalary months than necessary in 95 years, and if
these are dropped, we can have good adjustment. This
could have been done as follows :

In the first period of 30 years = 6 yugas, suppose
they had 11 intercalary months instead of 12.

The beginning of the yuga would go ahead of the
winter solstice in 30 years by 4'685 x 6 -28.110 days.

224

KBPOBT OF THE CALENDAR REFORM COMMITTEE

But if we do not have the intercalary month on the
30th year, the s/wgcr-beginning is brought back to
29.53-28.110^1.421 days before the W.S. day. The
same process is repeated for the next period of 30
years. The ?/wga-beginning is thus brought back to
2.842 days before the W.S. day.

The next period may be taken to consist of 35
years, i.e., 7 yttgas each of five years, in which the yuga-
beginning goes ahead by 3.264 days. The combined
result of the three periods of 30, 30, and 35 years is to
put the yuga beginning ahead of the W.S. day by 0.422
days only. Other conjectural cycles are described by
Dr. Shama Sastry.

But was any such practice really followed ? We
have no evidence from the verses ; but S. B. Dlksit
mentions that intercalary months were inserted only
when needed, and hence probably they were 'dropped
when not needed. 1

Tithis

The main object of the Vedaiiga Jyotisa calendar
appears to have been the correct prediction of the
tithi and nalcsatra on any savana (civil) day within the
yuga. In this respect, the rules were more accurate.
A tithi is defined as /^th of the lunar month. The
correct measure is

! uthi = ^0588 = 984353 daySi

while the measure taken = .983871 days. The
mistake is .000482 days on the lower side or one tithi
in 2075 days or in 5f years.

The five yearly period consists of 1830 civil days
in which there are 62 synodical months.

We know 62x29.53059 = 1830.8965 days. Hence
in order to make the tithi calculations correct, one day
(exactly 0.8965 days) had to be added to the total
number of civil days in the period.

Nakshatras

The days were named according to the naksatras or
lunar astensms in which the moon was found, and a
lot of crude astrology* had grown up round this
system. So it was necessary to predict the naksatra
in advance. The Vedanga Jyotixa calendar prescribed
some methods for such predictions.

In a five yearly period of 1830 days, the sidereal
revolutions of the moon amounted to 67 in which
there are 1809 aak^ntras*

Actually 1 naksatm day - 27 'g 166 = 1 .011913 days,

while the measure taken = H§§ = 1.011608 days.

♦Astrology based only on the sun and the moon. Later post-
Siddhantic astrology in India is largely (J race o- Chaldean, and makes
use of the si^ns of the -zodiac, and of planetary position and motion.

The mistake was .000305 days on the lower side or
1 naksatra in 3279 days or about 9 years.

The Time of the Vedanga Jyotisha

All recensions of the Veglanga Jyotisa contain the
following verses :

Svarakramete somarkau yada sakarii savasavau
Syatfcadadiyugam maghastapah suklo'yanarh hyudak. (6)
Prapadyete sravisthadau suryacandramasavudak
Sarpardhe daksiiiarkastu maghasravanayoh sada. (7)

These two verses taken together yield the following :
The winter solstice took place at the lunar
asterism &mm\ha, which is later called Dhani$\ha\.

This is the 21st naksatra in the Kfitikadi system
and 23rd in the Asvinyadi system and its component
stars are a, 0, y and 8 DelphinL* These stars are far
away from the ecliptic. We have for 1950 :

a Delphini, Long. = 316° 41' Lat. -+33° 2'

p m „ =315 39 y) -+31 55

y „ -318 40 n =+32 41

a „ „ -318 35 „ =+31 57

The Arabs have and i Aquarii which also
represent the Chinese Hsiu.

It has been stated in the Vedaiiga Jyoii$a that the
junction star of the asterism was placed at the
beginning of the division and it marked the beginning
of Uttarayana or the W.S. day. Thus the star
representing the Dhani§thd division had 270° as the
longitude at the time when the tradition of the Vedaiiga
Jyotisa calendar was formulated. If a Delphini is taken
as the principal star of the asterism, then its longitude
was 270° at the time of the Vedaiiga Jyotisa and in 1950,
its longitude is 316° 41'. As the solstices take about
72 years to retrograde through one degree, the time of
Vedanga Jyotisa is found to be (316° 41'— 270°) x 72-
46 °7 x72 = 3362 years before 1950 A.D. or 1413 B.C.
The star Delphini, however, yields a somewhat lower
period, i.e., about 1338 B.C.

The Plan of the Calendar

In a period of 5 years, there are :—
1830 civil days,

62 lunar months, and so 1860 tithis,
67 sidereal months and so 1809 nak§atras.
As the period contains 60 solar months, there are
2 intercalary months which are placed after every

* On a Dhani?tha day the moon got conjoined with both the
j3 and a Delphinis at interval of 2 hours.

INDIAN CALENDAR

225

30 lunar months. Thus in the third year, the month
Sravana is adhika which is followed by Buddha
&ravana ; and in the fifth year the last month is also
adhika which is adhika Magha,

There are 1860 tithis while the number of civil
days is 1830 ; so there are 30 omitted tithis {tithi ksaya).
Each period of 61 days contains 62 tithis, so one tithi
is omitted after 61 civil days. From this consideration
the number of civil days per month can be obtained
and will be shown in the table below. The Vedahga
Jyotisa people regularly counted a tithi to a day, but
after 61 days one tithi was omitted.

As regards naksatras, their number is 1809 in 1830
civil days, the difference being 21. So 87^ days weie
equivalent to 86y naksatras. They counted a naksatra
to a day successively, but after every 87 days (actually
87y days), one naksatra was repeated for two days.

The five different years of the period had
distinctive names, vi%., (1) Samvatsara, (2) Parivatsara,
(3) Idavatsara, (4) Anuvatsara, and (5) Idvatsara.

The plan of the five yearly calendar is shown
below :

Table 12.

Number of days in each month of the Vedanga
Jyotisa Calendar

Sain vat-

Parivat-

Idavat-

Anuvat-

Idvat-

sara

Magha 30

Phalguna 30

Caitra 29

Vaisakha 30

Jyais^ha 29

Asadha 30

$ravana {adhika) —

^ravana 29

Bhadrapada 30

Asvina 29

Kartika 30

Margasirsa 29

Pausa 30

Magha {adhika) —

29 or 30

Total No. of 355

354

384

354

383

days in the year

384

As already shown, the actual length of 62 lunar
months is 1830.8965 days, while there are 1830 civil
days in the five yearly period. It is therefore very
likely that one civil day was added to the period
when necessary to make it conform to the phases of
the moon which were regularly observed. This
additional day was no doubt placed at the end of the

period, and when it was added the last month adhika
Magha contained 30 days instead of 29 days which was
otherwise its due.

The ratio 1 for the duration of the longest day to
that of the shortest night given in the Vedahga Jyotisa
was first noted by Dr. Thibaut. Later the same ratio
was found by Father Kugler from Babylonian cunei-
form records of the Seleucidean period. The ratio is
characteristic of a latitude of 35° N, which is nearly
that of Babylon (for Babylon <p =32° 40'N). Hence it
has been inferred that the Vedahga Jyotisa-asttoxiomzTS
got this ratio from Seleucidean Babylon. But it may
be pointed out that the Vedic life centred round
North- Western India, from the SarasvatI valley
(Kuruksetra 0=29° 55') to Gandhar (^31° 32'N).
The ratios of the duration of daylight to night on the
summer-solstice day for different latitudes are as
follows :

Table 13.

Longest day and shortest night

(Calculated with obliquity of ecliptic as 23° 51' vhiqji is
for 1300 B. C. The results for 500 B. C. are also almost tha
same.)

Latitude

Longest day

Shortest night

Ratio

30° N

13 h 58 m

10 b 2 m

1,39

31° N

14 3

9 57

1.41

31° 32' N

14 6

9 54

1.42

32° N

14 8

9 52

1.43

32°40' N

14 12

9 48

1.45

33° N

14 14

9 46

1.46

34° N

14 19

9 41

1.48

35° N

14 24

9 36

1.50

It is seen from the above table, that even at the
latitude of Babylon, the ratio is not 1.50 but 1.45. At
Gandhar, it is 1.42. The difference is not very large.
But there is another factor to which attention must
be drawn.

Both Babylonians and Indians measured subdivisions
of the day by means of some kind of Clepsydra. A
description of the Clepsydra used by Indians during
the Ved&nga Jyotisa-petiod will be found in S.B. Dlksit*s
Bharatiya Jyoti&dtstra (Sec. II, Chap. I). But the day-
length must have been measured from the observed
time of sunrise to the observed time of sunset. This is
somewhat larger than the astronomical time of sunrise
on account of refraction. Assuming that the effect of
refraction is to elevate a celestial body near the horizon
by about 35', and the sun's semi-diameter is about 16',
the sun's upper limb appears on the horizon at a place
on 32° latitude, about 4 J minutes before the centre of
the sun is due on the horizon. For the same reason,
the sunset takes place 4£ minutes after the astronomical

226

KBPOBT OF THE CALENDAR REFORM COMMITTEE

calculated sunset. So the apparent length of the day
is increased by 2 x min. or by 9 minutes. Therefore
for the latitude of Babylon we have the length of
maximum day-light 14 h l2 m + 9- = 14 h 21 m , and the
night is 9 h 39 m . The ratio is now 1.49. Taking the
effect of refraction into consideration the ratio for
Gandhar also becomes 1.46, which is not much
different from 1.50 as for Babylon. So it is not
necessary to assume that the ratio was obtained from
Babylonian sources.

Effect of Precession

The Vedaiiga Jyotisa was prevalent for a long time
over India, for over 1300 years (1000 B.C. to 300 A. D.).
Hence it is likely that the subsequent astronomers
noticed the gradual shift of the solstitial colure in the
lunar zodiac. In fact, several references are found to
this effect. Garga, an astronomer whose name is
found in the Mahabharata, where he is described as
having an astronomical school at a place called
Gargasrota in the Sarasvatl basin, is the reputed author
of a pre-Siddhantic calendaric treatise called Oarga
Sainhita. He notes :

Yada mvartate'praptal.i sravisthamuttarayane

Aslesam daksine'praptab tada vindyanmaHad bhayam.

Translation : When at the time of Uttarayana
the sun is found turning (north) without reaching the
Sravisthas, and (at the time of Bahsinayana) turning
(south) without reaching the Mlesa, it should be
taken to indicate a period of calamity.

It shows that at the time of Garga the W.S. did
no longer occur in &ravis\ha, neither the S.S. occurred
in the Aslesa division. At the time of Vedaiiga Jyotisa
the two solstices were marked by the starting point of
&ravistha and the middle point of Mlesa respectively.
Garga therefore observed that the solstices were reced-
ing back over the lunar calendar, and had shifted at
least by half a na/c$a*ra-division from the middle of
A&lesa. His observations are therefore at least 480
years labst'than those of the Vedaiiga Jyotisa.

In the MaMbharata we get the following verse :

Asvamedha, Chap. 44,2
Ahal.i purvam tatoratrirmasah sukladayali smytali
Sravanadini rksani rtavab sisiradayali

Translation : Day comes first and then the night ;
months are known to commence with the bright
half, the naksatras with fcrpvana* and the seasons
with &iiira.

Here the asterism &ravana is described as the one
where the winter solstice takes place. Sravana is
just preceding &rav%8\ha and the solstices take about
960 years to retrograde through one naksaira division.

We get from this the time of composition of the
Mahabharata as about 450 B.C. or sometime earlier.

Varahamihira also notes that the winter solstice
no longer took place at Bhanis\ha,

PaHca SiddMntika, III, 21
A slesardhadaslt yada nivrttih kilosnakiranasya
Yuktamayanaih tadasife sampratamayanam

punarvasutalj.

Translation : When the return of the sun towards
the south ( i.e., the summer solstice ) took place from
the middle of Aslesa, the ay ana was right : at the
present time ayana begins from Funarvasu.

In his Bvhat Safnhita, an astrological treatise, he
records :

Bfhat Safnhita, . Ill, 1

Aslesardhatdaksinam uttaramayanam raverdbaniflthadyam
Nunam kadacidasit yenoktam purvasastresu.

Translation : The beginning of the southern motion
when the sun has passed half of Aslesa and the begin-
ning of the northern motion when the sun has passed
the beginning of Bhanis\ha, must have taken place
at some epoch ; for these are recorded in old treatises.

From the time of Vedaiiga Jyotisa to Varahamihira's
time the summer solstice moved through more than 1|
naksatras { i of Aslesa + Fusya ) which indicated a lapse
of more than 1500 years from the time of Vedaiiga
Jyotisa.

It is thus seen that the Hindu astronomers observed
the shifting of the cardinal points due to precession
of the equinoxes ; but as they had not developed the
sense of era, they were unable to find out the time-
interval between different records, and obtain a rate
for precession, as was done by Hipparchos. Their
observations were also crude, as they used only the
lunar zodiac. The shifting of the solstitial colures
remained to them an unsolved mystery.

5 5 CRITICAL REVIEW OF THE INSCRIPTIONS
RECORDS ABOUT CALENDAR

In this chapter, we are undertaking a critical
review of the references to the calendar in ancient
inscriptions, because, from the point of view of
accurate history, inscriptional records are far more
valuable than any references in ancient scriptures or
classics, as they are contemporary documents, which
have remained unaltered since the framers left them*.

* Sometimes inscriptions and copper plate records have been
found to have been forged at a latter date but such instances are
rare and can not escape detection by an experienced archaeologist

INDIAN CALENDAR

227

References in ancient scriptures, poems, epics and
other literatures are, on the other hand, very often
liable to alterations, interpolations and errors in the
hands of latter-day copyists and are, therefore, less
trust-worthy.

The oldest inscriptional records bearing a date
( barring those belonging to the Ind^is-valley period
which have not been deciphered ) belong to the reign
of the Emperor Asoka ( 273-236 B.C. ). From these,
wc can make fairly accurate deductions regarding the
calendar then in use.

We take the Fifth Pillar Edict, Rampurva version
found at the Champarai) district, Bihar. The
language is Asokan Prakrt, the script is the oldest
form of Brahmi. ( Sircar pp, 62-63 )

Fifth Pillar Edict — Rampurva Version

(1) Sadtmsatilva2mbhisitena(Sadv^

ktena) — * After twenty-six years had elapsed
since coronation'.

(2) Ti&u cdtufnmdlsl^u tisyafn pufnnamdsiyarn tint-

divasdni cdvudasafn painnadasafn 2>atipadafn

( Tisrsu cdtunndsisu tisydydfti pur^amdsydfn,

trisu divasenu-caturdase pancadase pratipadi

'On the three cdturmdsl days, on the tisya full

moon day, on the 14th, 15th and the first
day '

( On these and some other days, sale of fish is
forbidden).

Again, in the same :

(3) Athami-pakhdye cdvudasdye painnadawye

tisd ye pundvasune (Astami-pakse,

catur-dahjdfn, paftcadasydfn, tixydyd/n,
punarvasau ) j

'On the eighth paksa, on the 14th, and the
15th ( new moon ) on the Tisya and
Pimarvasu NaJcsatra days ,

(On these days, he forbids the castration of
bulls).

From these passages, we conclude that :
1. , No era was used, but regnal years ( number of
years elapsed since the king's coronation )
were used for dating.

2. The time-reckoning was by seasons, each of
8 paksas. The seasons are :

Grlsrna (Summer) : Comprising Caitra, Vaisdkha,

Jyai$tha, A$a4ha.
Var$a (Rains) : Comprising Srdvaya, Bhddra,

Asvina, Kartika.
Hemanta (Winter) : Comprising Agrahayana,

Pausa, Magha, Phdlguna.

3. The months are not mentioned by name, except
in one case where the month of Magha is
mentioned. They are purnimditta, i.e., they
started after full moon and ended in full moon.
This is not expressly mentioned but can be
inferred from the fact that the 14th, the 15th
(PaTicadasi) and the Pratipada, i.e., the first
tithi arc enjoined to be the days on which
certain actions are forbidden. These must be
the three days of invisibility of the moon, the
14th being before new moon, the 15th the
new moon, and the first, the day after new
moon, which were observed as unsuitable for
many particular performances.
4. The day reckoning was by the tithi (lunar day),
but the word tithi is probably not to be taken
in the sense of the present Siddhantlc tithi,
but in the sense of the Vedanga Jyotisa
tithi or the old Brahmanic tithi. In the latter
system, a tithi was counted from moon-set
to moon- set during the bright half, and from
moon-rise to moon-rise during the dark-half.
There was the same tithi for the whole day.
Prof. P. C. Sen Gupta has discussed this
method of tithi reckoning ( see p. 222 ).

5. Two days are mentioned by the lunar asterisms
Tisya (<s Cancri), and Punarvasu (/3 Geminonon),
As suggested one was probably his birth
naksatm, the other his coronation tmkmtra.
The days were therefore also named after the
naksatra. This system is found in vogue in
the epic Mahabhdrata, e.g., in the following
passage :

Balarama, the elder brother of Krsna, after returning
from pilgrimage on the eighteenth day of the battle
states :

M. Bh., Salya Parra, Ch. 34, 6

CatvariiiiHadalianyadya dve ca me nii.isi'tasya vai
Pusyena saihpraySfco'smi Sravane punaragafcah.
Translation : It is forty-two days since I left the

house. I started on the Pusya (day) and have returned

on the Sravana.

6. There is no mention of the year-beginning.
The Tisya Purnamasu i.e., the full-moon day
ending the lunar month of Paw$a is marked
out particularly.

It appears from the records that in Asoka's time,
the principles followed in framing the calendar were
those given in the Vedafiga Jyotisa. No era was used.
From the inscriptions, we can make no inference about
the luni-solar adjustment, but there is no doubt that
the year was seasonal as given in the inscription of the
Satavahanas (see next page).

a R.— 37

228

REPORT OP THE CALENDAR REFORM COMMITTEE

No records bearing a date of the imperial dynasties
following the Mauryas, the Sungas, and Kanvas
(186B.C.-45 A.D.) are known. But the next imperial
dynasty, the Satavahanas have left plenty of dated
records. In these, the same system of date-recording
by regnal years, the seasons, the paksas, and Uthis are
found. There are 8 pak,as in a season of four months,
and they were serially numbered from 1 to 8. The
odd ones were KfW paksas, the even ones bukla
pak§as.

Some examples are given below :
(1) Nasik Inscription of the Satavahana Emperor,
Gautamiputra Sri Satakarni (Sircar, pp. 192-93).

Data paiika Savachare 10 + 8 vasapakhe 2 dimse 1
(datta pa\tika Sar'nvatsare a^Uase 18 Varsapakse
divtiye 2 divase prathame 1).
i c the inscription was recorded in the eighteenth
year elapsed since the coronation on the first day
of the second Pak$a of the Vam season, i.e., in the
lunar month of Sravaw> on the first day after new
moon (&ukla pak$a).

There are other Satavahana inscriptions similarly
dated as summarized in the table below :

Table 14.

Table of Inscriptions of Satavahana Kings,
showing date-recording.

Lliders

1024 Ratio Gotamiputasa Sami-Siriyaiia-

Satakanisa ^ 16_G 1-5

1100 Ba5o Vasithiputaaa Sami-Sm-Pulumavisa 7-G 5-1
1106 R. V. Siri-Pulumavisa ■■■ 2 ^-H 3-2

1122 B. V. Siri-Pulumayisa . •-• < >G

1123 R. V. Siri-Pulumayisa •■■ iy "^

1124 R. V. Siri-Pulumavisa ••■ u-vi^-i*

22-G 1-7

1126 R. G. Satakanisa ^ 24 "^ A ' 6

1146 R. G. Sami Siriyatia Satakanisa ... 7-H

1147 R. y. Sami Siri-Pulumaisa ... 2 ' H 8
90 (Sircar )- Siri-Pulumavisa ... 8 " H 2 ' 1

B means ratio, V-Vasithiputasa, G -Gotamiputasa.
The number in the first column indicates the serial
number of the inscription in Lliders list. The last
column contains dates, in an abridged form ; e.g., in
1123, we have 19, G 2-13. Here 19' is the regnal year,
G denotes Orima or summer season, *2' following G
denotes the second prim i.e., the second half of the
month of Caitra, constituting the &ukla pak$a, and the
last numeral 13' denotes the day. But it is not clear
whether the day is the lunar day, i.e., the tithi or the
solar day. Even if it be the tithi, it is probably not
the Siddhantic tithi, but the old Brahmanic or Vedafiga
tithi.

According to our calculations, the date of Gautami-
putra Satakarni would be about the first century A.D.
We take some still later records.

(2) Raja Vlrapuru§adattaof Nagarjunlkon4a (Sircar,

pp. 220-221)

llainTto Siri VirapurisadaUw Sava d va pa 6 di 10
(Rajnuh &rt Vtrainmt.yt<latta*ya safnvaisme
msthe a varsapalse sasihe (> divase damme 10,
On the sixth year of King Sri Virapuru§adatta on
the 6th pah-va of the rarsa season, on the tenth day.
The sixth of var*a pakta is month of Ssvina, second or
light half (Sulda paksa).

It is obvious from the above inscriptional evidences,
that continuous era-recording was not used by Indian
dynasts up to the time of the Satavahanas, and no
ancient books, not even the Mahabharata mentions
an era.

As no era is mentioned, it has been difficult to work
out a chronology of the early Indian dynasts including
the Satavahanas.

The Coming of the Era to India

As we have seen in § 3.5, the era reckoning had been
in use in Babylon since 747 B.C., and the Seleucidean
era which marked the accession to power ot Selcucus
at Babylon in 312 B.C., was widely current m the
whole of the Middle East, both by the royalty and
the public.

But though as Asoka's Girnar inscription says that
he was in diplomatic correspondence with five Greek
kings of the West, including Antiochus I and II of
Babylon, and the Ptolemy of Egypt, and sent Buddhist
missionaries to these countries, it is clear from his
records that he continued to use the purely Indian
methods of date-recording based on the Vedaiiga-Jyotw*
There is not the slightest indication that any of the
Indian imperial dynasties which followed the Mauryas,
ti*, the Sungas and Kanvas (186 B.C. -45 A.D.). the
Satavahanas ( 100 A.D.) allowed themselves to be
influenced by the Graeco-Chaldean luni-solar calendar
which was then in vogue in the Near East.

From about 180 B.C., North-Western India having
Taxila as capital passed under the Bactrian Greeks.

It is rather strange that though we have plenty of
coins of the Bactrian Greeks who ruled in Afghanistan
and N.W. India between 160 B.C., and 50 B.C., from
which their names have been recovered, and some
kind of chronology has been worked out, not a single
record has yet been discovered which bears a date,
except two doubtful ones. One is the coin of a
certain Plato, found in the Kabul valley, which bears
certain symbols which have been interpreted as 147
of the Seleucidean era, i.e., 165 B.C., Plato has been

INDIAN CALENDAR

229

identified by Tarn to be a brother of Eucratidas,
founder of the second Greek ruling house (175 B.C.-
139 B.C.) in Bactria. But the interpretation is
doubtful.

The second one is an inscription of the time of
king Menander, the great king of the Euthydemid
house who ruled over the Punjab, Sind and Rajputana
about 150 B.C., on the Shinkot Steatite Casket, the
only one of the Greek kings who has found a
permanent place in Indian literature in the celebrated
Milinda Pafhho, a philosophical treatise meaning
questions of king Menander. The inscription referred
to mentions regnal year 5, the Indian month of
Vaisakha, and the twenty-fifth day. Thus the date-
recording is Indian, but slightly different from the
system used in Asokan or Satavahana inscriptions
because the. paksa is omitted.

Our studies gi ven in § 3 3, shows that a mathe-
matically accurate luni-solar calendar, based on
astronomical knowledge, was first evolved in Seleucid
Babylon between 300 B.C. to 200 B.C. by Chaldean
astronomers. The features of this calendar were :

(a) The use of the Seleucidean era for numbering
years in place of the regnal years.

(b) The beginning of the year with the lunar month
.of Nisan which was to start on a date not later than

a month of the vernal eqxinox.

(This corresponds to the Indian month of Vaisakha
later defined in Siddhantic calendars).

(c) There was an alternative method of starting with
the Greek month of Dios which was to begin on a
date not later than a month of the autumnal equinox.

(This corresponds to the Indian month of Kartika,
as later defined in Siddhantic calendars).

(d) Luni-solar adjustment was done by the nineteen-
year cycle (vide § 3*2 — 3'4).

This system of date-recording spread far and wide
in the Near East and was adopted by other ruling
dynasties, viz., the Parthians, who however used an era
starting from 248 B.C. They used Macedonian months
without alteration.

I* can now be shown that this system penetrated
gradually into India.

Era or eras of unknown origin began to be
mentioned in certain inscriptions found in the North-
Western Punjab and the Kabul valley about the first
century B.C. Some of them mention kings belonging to
the Saka tribes who ruled Ariana (west and southern
Afghanistan comprising the Herat regions-Area), the
Kandahar regions (Arachosia), and Gandhara (N.W.
Punjab) between the second century B.C. and the first

century A.D. The inscriptions are mostly in Kharo'sthl
and later ones found on Indian soil are in Brahml. The
Kharosthl inscriptions are collected by Dr.Sten Konow
in his monumental work Cm*pus Inscriptionum
Indicarum, Vol. II., Part I., and are reproduced below
in Groups A and B.

Group A is identical with Konow's A (with the
omission of Nos. 20-23) and contains dates from year
58 to 200. Group B, identica with Konow's B-Group,
contains the inscriptions of Kusana period bearing
dates of years between 3C0 and 400.

GROUP A

1. Maira : [sain

2. Sahdaur A : ra\_ja] no Damijadasa saka-sa.

[$a${«\..6'0].

(Reading uncertain.)

3 . Sahdaur B : [ maharayasa ? ] Ayasa sain ....

4. Mansehra : . .aq[hasathi....

5. Fatehjang : sain V>\9 Prothavatasa masasa divase

sodase 10.

6. Taxila copper-plate : sainratsaraye athasatatimae

78 maharayasa mahaintasa Mogasa Panemasa
masasa divase pafneame 5 etayc purvaye.

7. Mucai : vase ekasitimaye 8 I.

8. Kala Sang : [sain 10i)\ Reading uncertain.

9. Mount Banj : sainvatsaraye 102.

10. Takht-i-Bahi : maharayasa Guduvharasa vasa

26 safnvatsarae tisatimae 103 Vesakhasa
masasa divase [praiha] »ne [di 1 atra pwria']
pak ne.

11. Paja : safnvatsaraye ekadasa [*a»] timaye 111

Sravanasa masasa di [m*] se painlcada^se 15.

12. Kaldarra : vasa 113 Sravanasa 20.

13. Marguz : [vase 1*~\17.

14. Pan j tar : sain 122 Sravanasa masasa di praclhame

1 maharayasa Ousanasa rajami.

15. Taxila silver scroll : sa 130 ayasa Asa4asa

masasa divase 15 isa divase . . maharajasa
rajatirajasa devaputrasa Khttsanasa aroga\
daksinae.

16. Pesawar Museum, No. 20 : sain 108 Je\hamase

divase pafneadase.

17. Khalatse : sain 187 maharajasa Uvimaka [vthi~\

sasa.

18. Taxila silver vase : ka 191 maharaja ibhrata

Manigulasa putrasa^Jihonikasa Cvkhsasa
k$atrapasa.

19. Dewai : sain 200 Vesakhasa masasa divase

athame 8 itra khavasa.

230

REPORT OF THE CALENDAR REFORM COMMITTEE

The Method of Date Recording

A record fully dated in Group A gives :

The year of the era in figures and words ; though
it does not give any particular designation to the era.

The month, mostly in Sanskrit ; the day, by its
ordinal number, e.g., No. 11, which means in the year
111 on the 15th day of the month of Sravaria.

The months are all in Sanskrit, except in No. 6, in
which the month is in Greek (Panemos = Asatfha). No.
6 alone of this group contains the rather mysterious
phrase 'Etaye purvaye' which means, 'before these*.
This phrase, the meaning of which is not clear, occurs
in Kusana (Group B) and even in Gupta inscriptions.

This method of dating is quite different from that
of the contemporary Indian dynasts, viz., the
Satavahanas, which mentioned regnal years, the season,
the paksa, and then probably the old tithi or the lunar
day. But it agrees with the method followed in
contemporary Parthia, which mentions the year
usually in the Seleucidean era, rarely in the Arsacid
era, the name of the month in Greek, and the ordinal
number of the day, which ranges from 1 to 30 (see
Debevoise, 1938). From No. 10, it appears that
whenever Indian months were used they were
Purnwianta, following the classical Indian custom.

Date of records of Group A

None of the inscriptions of Group A appear to
be 'Royal Records' but some contain names of kings,
e.g., No, 6, which mentions a Maharaja Mahainta Moga,
who is taken to be identical with a king whose coins
have been found in large numbers in Gandhara. He
calls himself 'Maues' in the Greek inscription on the
obverse, and Moasa (i.e. of Moa) in Kharosthl on
the reverse. The title given there usually is
Maharajasa Eajatirajasa Mahafntasa. It is held that
King Moga was Saka leader who starting from a base
in Seistan or Arachosia, invaded Gandhara through the
southern route, sailed up the Indus, and ousted the
Greek rulers Archebius from Taxila, Artemidorus
from Puskalavati and Telephos from Kapsa (Bachhofer,
1936) and founded a large empire comprising parts of
Afghanistan, Gandhara and the Punjab.

He is generally held to have been a Saka, but some
hold without sufficient reason that he was a Tarthian.
He is the first of Indo-Scythian kings known to
numismatics. He was followed by other Indo-Scythian
kings in Gandhara; who are known from wide variety
of coins issued, viz., Azes I, Azilises and Azes II.
But there is no clear reference to them in these ins-
criptions except the word 'Ayasa' in Nos. 10 and 15,

which is supposed to stand for Azes. But this has
been disputed-

This series starts with the year 58, if Cunningham's
reading of (1) with the additional reading of the king's
name 'Moasa' is accepted. But even if we reject it,
the series certainly starts with the year 68 in No. 5,
and goes up to 136 at fairly small intervals, then to
168, 187, 191, 200 containing names of rulers known
from coins, viz., besides Maues above mentioned,
Gondophernes (103 = 20 B.C.), some Kusana king (122
= 1 B.C.), Devaputra Kusana (136 = 14 A.D.), Maharaj-
bhrata Jehonika (191=69 A.D.). They are held to be
dated in the same era, which is usually called "the Old
Saka Era, shortly called O.S.E. But up to this time,
there has been no unanimity amongst scholars about
the starting date of the era used in inscriptions
grouped under A.

We now take the second group of inscriptions
which are those of the Kusanas, who ruled in North
India in the second century A-D.

GROUP B
The Ku§ana Inscriptions after Kaniska :

24. Kaniska casket : sain 1 ma[ harayasa ]

Kaniskasa.

25. Sui Vihar : maharajasya rajatiraja&ya devapu-

trasya Kaniskasya safnvatsare ekadase sain
11 Baisi{rn)kasya masas[ y ]a divase( in)
athavise 28 1 [ ay a ] tra divase.

26. Zeda : sain 11 Asa4asa masasa di 20 Utara-

phagune isa kswnami murotiasa

marjhakasa Kaniskasa rajami.

27. Manikiala : saM 18 Kartiyasa majh [ e ] divase

20 etra purvae maharajasa Kaneskasa.

28. Box lid : sain 18 masye Arthamisiya sastehi 10

is [ e ] ksunaftimri.

29. Kurram : sain 20 masasa Avadunakasa di 20

is [ e ] ksunainmi.

30. Pesawar Museum, No. 21 ; maharajasa [Vajus]

kasa sain [24 Jethasa*!] masasadi ise

ksunaMmi.

31. Hidda : sainvatsarae athaviinsatihi 28 masye

Apelae sasiehi dasahi 10 is [ e ] ksunainmi,

32. Sakardarra : sain 40 P [ r ~\o\havada$a masasa

divas[ami~\ visami di 20 atra divasakale.

33. Sra : maharajasa rajatirajasa devaputrasa kaisa-

rasa Vajheskaputrasa Kaniskasa sainvatsarae
ekacapar[ i )sa[ i ] sain 4 1 Jethasa masasa di
25 is [e] divasaksuiiami.

34. Wardak : sain 51 masy[ e ] Arthamisiya

sastehi 15 imena ga<trigrena maharaja

rajatiraja Eoveskasra agrabhagrae.

INDIAN CALENDAR

231

35. Ui)4 : sain 61 Cetrasa mahasa divase athanii

di S iia k§unami Purvaxa4e.

36. Mamane Dheri : sain S9 Margasirasra masi 5 ise

Jc§unami.

An incomplete date, makasa di 25, is further
found in the Kaniza Dheri inscription.

The second group Nos. 34-36 contains Kharosthi
inscriptions of the Kusana kings after the first Kaniska.
These and Kusana Brahmi inscriptions mention :

Years from '1 to 9a the kings Kaniska I from
lto24,

Vajheska from 24-28, Kaniska II of the

year 41>
Huviska from 33-60,
Vasudeva from 62-98
The King's name and the titles are given in full,
and in the genitive. The era is generally ascribed
to the famous Kaniska as we have a record of his first
year.

Their method of date-recording is the same as in
Group A, viz., ( see No. 25 ) the year of the era, the
month name in Greek or Sanskrit, the ordinal number
of the day* then the phrase equivalent to asyai'n
purvayaM ( before these ), but in these inscriptions,
it is expressed in the form ise kxunawi or its variant,
which has been interpreted by Konow as equivalent
of asyafn or etasijafn pUrvatjain in the Khotani Saka
language which Konow thinks was the mother tongue
of kings of the Kaniska group and which they use in
their inscriptions. In fact kings of this group use
a number of Khotani Saka words, and from their wide
range of coins are known to have put in a medley
of Greek, Iranian, and Indian gods including Buddha
on their coins, but the names of the gods are not in
their original Indian, Iranian or Greek form but invari-
ably in the form used in the Khotani Saka language.

The method of date-recording followed by the
Kusanas, in spite of its identity with that of Group A
shows some interesting variations. In the Kharosthi
inscriptions of the Kusanas, the months are mostly
Greek, less so in Sanskrit ( Caitra, Vaisdkha, etc. ).
The days run from 1 to 30 and clearly they are not
tithis but solar days. When we turn to Brahmi inscrip-
tions, we find that the month names are mostly
seasonal : Oiima, Var$d, or Hemanta as in the Satava-
hana records. But since 4 is the maximum number
attached to these, and the day numbers run from
1 to 30, the number after the season denotes a month,
not a pak$a and the days are solar. Thus G 4 denotes
the fourth month of the Gri$ma season, viz, A$a<lha,
and not the fourth pah$a as was the case with the
SatavShanas which would be the second half of
Vai&kha. The pak$a is given up.

This is a deviation from Satavahana method of
date-recording and follows closely the Graeco-Chal-
dean method. Some inscriptions mention Greek
months ( e. g. Gorpiaios which is Asvina or Bhadra
in Sircar's No. 49, p. 146 ) others Indian lunar months
( e. g. Srarana in No. 51 ), but their number is small
compared with the seasonal mode of recording months.
These inscriptions give no indication as to whether
the month is Purijimanta or Amanita. The Indian
months are Puruiviattta.

But the Zeda inscription of year 11 ( No. 26 of
Group B) mentions that the imhsatra was TJUaraphalgurd
on the 20th of Asdiiha, and ( 35 ) mentions that in
the year 61, the mikmtra on the 8th day of Caitra was
Pnrvasadha. A comparison with tables of naksatra*
shows that the months ended in full moon {Purr^imdnid).
As purnimanta months were unknown outside India,
the Kusanas must have yielded to Indian influence
and adapted their original time-reckonings to the
Indian custom; at least in their use of Indian months.

Historians and chronologists now almost unani-
mously hold that all these inscriptions of Group B are
dated in the same era which is sometimes called the
Kusana era, which was founded by King Kaniska.
This is said to be proved by the fact that the inscrip-
tions range from year 1, and we have phrases as in
No. 25 of the Maharaja Bdjddhirdja Devaputra
Kani$Jca, in the year 11. But a little more scrutiny
shows that it is only a conventional phraseology, used
in almost all Kusana inscriptions, for even in as late
a^s an inscription of year 98 of this group, we read 'of
the Maharaja Vasudeva in the year 98\ ' It is therefore
by no means clear that such phrases can be interpreted
to *nean that Kaniska started an entirely new era.
In fact, from Kaniska s profuse use of Greek months
and Greek gods, in his inscriptions and coins,
Cunningham was led to the belief that Kaniska dated
his inscriptions in the Seleucidean era, with hundreds
omitted, so that year 1 of Kaniska, is the year 401
of S. E. and year 90 of the Christian era.

But it has been known for some time that the
Kusana empire did not stop with that Vasudeva who
comes after Huviska. Dr. L. Bachhofer (1936) has
proved from numismatics the existence of :

Kaniska III, reigning apparently after Vasudeva I,
Vasudeva II, reigning after Kaniska III.
The kings appear to -have retained full control of
the whole of modern Afghanistan including Bactria
which appears to have been the home land of the
Kusanas and some parts of the Punjab, right up to
Mathura.

There is yet no proof for or against the point that
they retained the eastern parts, after year 98 of Kusana

232

EEPORT OF THE CALENDAR REFORM COMMITTEE

era. Herzfeld had established that Vasudeva II,
who appears to have come after Kanaka III .about
210 A.D., was deprived of Bactria by Ardeshir I, the
founder of the Sasanid dynasty of 'Persia. The
Sjsanids converted Bactria into a royalvprovince under
the charge of the crown prince, who struck coins
closely imitating those of the Kus5nas. Vasudeva II
is also mentioned in the Armenian records of Moise of
Khorene, a Jewish scholar, under the name Vehsadjan,
as an Indian king who tried to form a league with
Armenia and other older powers against the rising
imperialism of Ardeshir. Vasudeva II is also thought
to have sent an embassy to China about 230 A.D *.

The second Sassanian king Shapur I, claims to have
conquered sometime after 240 A.D. l PSKVR% which has
been identified with Puru§apura or Peshawar, the
capital of the KusSnas. This has also been confirmed
by the French excavations at Begram (Kapi£i) in
Afghanistan, which was destroyed by Shapur between
242 and 250 A.D. But this probably was not a
permanent occupation but a raid, as a Ku§ana king
or Shah is mentioned in 'the Paikuli inscription of the
Sasanid king Narseh (293-302 A.D.).

Kushana Method of Date-recording In India :

It appears rather strange that the Kusana way of
date-recording should suddenly come to a dead stop
on Indian soil with the year 98 of Vasudeva I, and no
records containing a year number exceeding 100 should
be found on Indian soil.

The mystery appears now to have been successfully
solved by Mrs. Van Lohuizen de Leeuw in her book
The Scythian Period (pub. 1949). She has proved that
several Biahml inscriptions in the Mathura region bear
dates from years 5 to 57 in which, following an old
Indian practice, the figure for hundred has been
omitted. Thus k 5 T stands for 105, '14' stands for 114
of the Kusana era. The following example will suffice
(vide pp. 242-43 of the Scythian Period).

Cue and the same person Arya Vasula, female
pupil of Arya Sangamika, holding the important
position of a religious preacher in the Jaina community,
is mentioned in two Brahmi inscriptions (No. 24 and
No. 70 of Lliders) bearing the year designations of 15
and 86 respectively, the date-recording being in the
typical Kusana style. The palaeographical evidence
also shows that the inscriptions were recorded in the
Kusana age, though the name of the reigning monarch

* Ghirshman thought that the Viisudev* Kusana of these
references is Vasudeva I, whose last reference is year 98. He equated
year 98 of Kanaka's era to year 242-250 A.D., and arrived at the
date 144 to 152 A.D. for the initial year of the Kanaka era. But the
equation of this Vasudeva with Vasudeva I is certainly wrong. This
must be Vasudeva II, or may be a still later Vasudeva.

is not mentioned. Now it is clearly impossible that
the same person would occupy such an important
position from the year 15 to 86, a period of 71 years.
L. de Leeuw therefore suggests that while 86 is the
usual Ku$ana year (reckoning from year 1 of Kaniska),
'15' is really with hundred omitted and represents
actually the year 115 of Kaniska, i.e., dates of the two.
inscriptions differ by 115-86 = 29 years, which is much
more plausible. In other words, after the year 100 of
the Kanaka era was passed, hundreds were dropped
in inscriptions found near about Mathura.

The author has sustained her ground by numerous
other illustrations, and there seems to be no doubt
that this is a brilliant suggestion and it can be taken
as proved that in numbering years of an era, hundreds
were omitted in certain parts of the Kusana dominion
in the second century of the Kaniska era. L. de
Leeuw has found such dates in no less than 7 instances
bearing years 5, 12, 15, 22, 35, 50, 57 in which
apparently 103 has been omitted, so that 57 really
stands for 157, and if we take the Kaniska era to have
started from 78 A.D., the date of the last one is A.D.
235 = (157 + 78). Probably the name of the reigning
king was not mentioned, as he had either lost
control over these regions, or as the inscriptions were
religious, it was not considered necessary. The second
alternative appears to be more correct.

This is supported by the inscription on an image
discovered by Dayaram Sahni in Mathura in 1927.
It mentions Maharaja Devaputra Kaniska. But on
palaeographic grounds, he can neither he Kaniska I
(1-24) nor Kani§ka II (41), but a later Kaniska, coming
after Vasudeva I, and 14 is really year 114 of the
Kaniska era. We may identify him with Kaniska
III of Bachhofer.

So we come to this conclusion :

The records of Ku?ai)a kings, after Kaniska I
range from year 1 to 98. In the second century of
the Kaniska era, hundreds are omitted and such
records have been found up to year 157, i.e., year 235
of the Christian era.

This raises a strong presumption that Kaniska
was not the founder of the era, but he used one
already in vogue, but omitted the hundreds. Thus
year 1 of Kaniska is really year 1 plus some hundred,
may be 1, 2, or 3. L. de Leeuw does not expressly
suggest this, though it is apparent from her reasoning
that year I of King Kaniska is year 201 of the Old &aka
era*. If this suggestion be correct, since the old Saka
era is taken to have started in 123 B.C. ( — 122 A.D.)
instead of in 129 B.C., -as postulated by L. de Leeuw,
Kaniska started reigning in ( 201-123 )«78 A.D.

* The suggestion is of Prof. M. N. Saha.

INDIAN CALENDAE

233

From the above review of inscriptional records and
contemporary history, the following story has been
Teconstructed.

(1) The Saka era was first started in 123 B.C.
when the Sakas coming from Central Asia due to the
pressure of HOnas wrested Bactria from the Parthian
emperors after a seven years' war. The leader was
probably one 'Azes', and therefore the era was also
alternately called the 'Azes' era. This Azes is not to
be confounded with the two later Azes who succeeded
Maues and reigned between 45 B. C. to 20 B. C.
Earlier Sakas used Macedonian months and Graeco-
Chaidean method of date recording, prevalent
throughout the whole of Near East. In Indian
dominions, Indian months which were equated to
Greek months were used. As their coins show, the
xuling class had adopted Greek culture. /

(2) When the Sakas spread from 'Sakasthan , i.e.,
modern Afghanistan into contiguous parts of India,
they began to be influenced by Indian culture. During
the first stage, they exclusively used Greek in their
coins, but later they began to use Kharosthi and
Brahml as well. The coins of Maues (80 B.C.-45 B.C.),
Azes I, Azilises, Azes II show increasing influence
of Indian culture. The southern Sakas who penetrated
into Saurashtra and Malwa show Indian influence to
a greater degree.

(3) In the first three centuries, they (Maues group,
Nahapana group and Kusanas) used the old Saka era
-omitting hundreds, and using a method of date-
recording which was an exact copy of the contem-
porary Graeco-Chaldean system prevalent throughout
the Parthian empire (Macedonian months, and
ordinal number of days). But they also began to use
Indian months. Whenever they did it, the month
was Purnimania, as was the custom with old Hindu
dynasts (Mauryas and Satavahanas).

(4) The classical Saka era starting from 78 A.D.
is nothing but the old Saka era, starting from 123 B.C.
with 200 omitted, SO/ that the year 1 of Kaniska is
year 201 of the Old Saka era.

&aka Era in the South- West.
Besides the earlier Sakas belonging to the Maues
group, and the Kusanas, there was another groupof Saka
kings, who penetrated into the south-western part of
India! The earliest representative of this group was
Nahapana and his son-in-law Usavadata. Their
records are dated in years 41 to 46 of an unknown era.
They use Indian lunar months and days (probably tithis).
These Sakas ruled in Rajputana, Malwa, and northern
Maharastra and were engaged in continuous warfare
with the Satavahana ruler Gautamlputra Satakarni
who claim to have destroyed them root and branch.

The senior author has shown that Nahap3na used
the old Saka era with one hundred omitted, so that
the year 46 of Nahapana was the year 146 of the old
Saka era or about 24 A.D.

The Satavahana kings Gautamlputra Satakarni and
his son Vasisthlputra Pulumavi, whose records are
found dated in the typical Indian fashion, reigned
according to his hypothesis from about 40 A.D. to 80
A.D. From epigraphical record, Nahapana is at least
separated by about 100 years from the next group of
Saka rulers, the Sakas of U]jain belonging to

the house of Castana,

The Saka satraps of Ujjain.
We come across the records of- another Saka ruling
family, reigning in Ujjain.

[Andau (Cutch) stone inscriptions of the time of
Castana and Rudradaman, Sircar, p. 167].

Rajnah Castanasya Jdmotika-putrasya rajfiah Jludra-
damnah Jaymldma-putrasya [ca] var$e diipaftcase 52
Phalguna-bahulasya { = krsna-pak$asya) dvillya vare
{^divase) 2 tnadanena Sifnhila-putrena bhaginyah
Jyes thaviraya h Sifn hila-duhitu h aupasati sagotraya h
yastih utthdpita- •• .

Translation: Of king Castana, son of Jamotika
and of king Rudradaman son of Jayadaman, in the year
52, on the dark half of the month of Phalguna and on
the 2nd day *'

This inscription mentions the year 52, the second
day of the Kfsna paksa of the month of Phalguna.

There is no doubt that the year mentioned is that
of the &aka era as now known. For this satrapal house
reigned continuosly for nearly 300 years and has left a
wealth of dated records. But the name of the era is
not mentioned in the earlier records. They are
mentioned merely as years so and so. ^

The earliest authentic instance of the use of Saka
era by name is supplied by the Badami inscription of
Calikya Vallabhesvara (Pulakesin I of the Calukya
dynasty), dated 465 of the Saka era {&aka-Varsesu
Catus-s-atesu paftca-sasthi-yutesu : Epigraphia Indica
XXVII, p. 8J. In literature the use of the era by name
appears still earlier. The Lokavibhaga of SimhasOri, a
Digambara Jaina work in Sanskrit is stated in a
manuscript to have been completed in 80 beyond 300
(i.e. 380) of the Saka years (Ep. ImU XXVII, p. 5).
There is no doubt that the era used in the records of
the western satrapal house beginning with Castana
and Rudradaman have come down to the present times
as the Saka Era, which is the 'Era' par excellence
used by Indian astronomers for purposes of calculation.
There ere 30 or more 'Eras' which have been in use
in India {vide § 5*8), but none of them have been

234

REPORT OF THE CALENDAR REFORM COMMITTEE

used for calendarical calculation by the Indian

astronomers. /

Yet it is difficult to assign the origin of the Saka
era to the western satraps. An era can be founded
only by an imperial dynasty like the Seleucids, the
Parthians or the Guptas. The western satraps never
claim, in their numerous records, any imperial position.
They are always satisfied with the subordinate titles
like Ksatmpa {Satrap) or Maha Ksatrapa (Great Satrap)
while the imperial position is claimed by their
northern contemporaries, the Kusanas.

The conclusion is that the western Ksatrapas
used the old Saka era, with 200 omitted ; so that year
1 of the present Saka era is year 201 of the old Saka
era, i.e., (201— 122) = 79 A.D.

The gradual adoption of characteristic Indian
ideas by the Sakas is shown in a record of Satrap
Rudrasimha dated 103 S.E. or 181 A.D.

[Gunda Stone Inscription of the time of
Rudrasimha I, Sircar, p. 176]

Siddham. Rajnah mahdksatrapasya svdwi-Castana-
prapautrastja rajnah kmtravasya svaml Jayaddmavaittrasya
rajnah mahdksatrapasya srdmi-Rudraddma'Putrasya
rajnah ksatrapasya svdmi-Rudrasifnhasya varse tryutta-
ra&ata (tame) ( = adhika) 103 Vaisdkha snddhe
( = suklapakse) paftcama-dhanya tithatt Rohint naksatra-
muhurte abhirena senapati Bappakasya put rem senapati
Rudrabhutind grame rasapadrake vapi ( = kvpah)
khanita, bandhitd [stladibhih] ca sarva sattvanafn hita-
mkharthaw iti.

Translation : Of king Mahaksatrapa of Svaml

Rudrasimha in the year 103 in the light half of the
month of Vaisakha on the 5th tithi and in the Rohirji
naksatra muhurta,

The Saka satrap Rudrasimha, reigning in 181 A.D.
thus dates his inscriptions using an era (the Saka era),
purely Indian months, tithis and naksatras. This is
in full Siddhantic style, because the characteristic
features of Siddhantic method of date recording which
mention ////// and naksatra are first found in this
inscription. The 'week day' is however not mentioned.

This is first mentioned in an inscription of the
emperor Budhagupta (484 A. D.).

Sate pauaiyixtyadhike varsauam bhupatau ca
' Budhagupie Asddha rndsa [sukla~] — [f/m] dasyain
miagurordhase

(Iran- Stone Pillar Inscription of Bndha Gupta —
Gupta year 165-484 A.D.).

Translation ; In the year 165 of the Gupta era
during the reign of emperor Budhagupta in the month
of Asadha and on the 12th tithi of the light half which
was a Thursday (i.e. day dedicated to the preceptor
of Gods).

5.6 SOLAR CALENDAR IN THE SIDDHANTA

JYOTISHA PERIOD
Rise of Siddhantas or Scientific Astronomy

The Vedahga Jyotisa calendarical rules appear,
from inscriptional records, to have been used right up
to the end of the reign of the SatavShanas (200 A.D.).
The analysis of inscriptional data on methods of date-
recording given in § 5*5 shows that it was the Saka
and KusSna rulers (50 B.C. - 100 A.D.). who introduced
the Graeco-Chaidean methods of date-recording,,
prevalent in the Near East into India. These methods
require a knowledge of the fundamentals of astronomy,
which must have been available to the Saka and
Kusana rulers. In India, as the inscriptional records
show, some purely Indian dynasts probably accepted the
system in full from about 248 A.D. (date of foundation
of the Kalachuri era, the earliest era founded by Indian
kings, leaving aside the Saka era which is admittedly'of
foreign origin and the Vikrama era whose origin is still
shrouded in mystery). During the time of the Guptas
who founded an era commemorating their accession to
power in 319 A.D. the integration of the western
system with the Indian appears to have been complete.

Indian astronomical treatises, explaining the rules
of calendaric astronomy, are known as Siddhantas, but
it is difficult to find out their dates. The earliest
Indian astronomer who gave a date for himself was the
celebrated Aryabhata who flourished in the ancient
city of Pataliputra and was born in 476 A.D.

It is necessary to reply to a question which has
very often been asked, but never satisfactorily
answered, vi,\.,

Why did the Indian savants who were in touch with
the Greeks, and probably with Greek science since the time
of Alexander's raid (323 B.C. \ take about 500-600 years
to assimilate Greek astronomy, and use it for their own
calendar- framing ?

The Indians of 300 B.C. to 400 A.D., were quite
vigorous in body as well as in intellect as is shown by
their capacity to resist successive hordes of foreign
invaders, and their remarkable contributions to
religion, art, literature and certain sciences. Why did
they ,not accept the fundamentals of Greek astronomy
for calendarical calculations earlier ?

The reply to this query appears to be as follows :

The Greeks of Alexander's time had almost nothing
to give to the Indians in calendaric astronomy, for
their own knowledge of astronomy at this period was
extremely crude and far inferior to that of the
contemporary Chaldeans. The remarkable achieve-
ments of the Greeks in astronomy, and geometry,.

INDIAN GALEUMfl

235

though they started from the time of Alexander
(Plato's Academy), really flowered in full bloom in the
century following Alexander (330 B.C. -200 B.C.).
The culmination is found in. Hipparchos of Rhodes
who flourished from 160—120 B.C. ; he wrote treatises
on astronomy. Simultaneously in Seleucid Babylon,
Chaldean and Greek astronomers made scientific
contributions of the highest order to astronomy ( vide
§ 4.7 & 4.8 ), but none of their works have survived, but
are now being found by archaeological explorations.

It is therefore obvious that the Indians of the age
of Asoka (273 B.C.— 200 B.C.), who were in touch with
the Greek kingdoms of Babylon and Egypt, had not
much to learn from the Greeks in astronomy.

The Mauryas were succeeded by the Suhgas
(186 B.C.— 75 B.C.), but Indians during this age were in
touch only with the Bactrian Greeks. But by this time,
the Parthian empire had arisen (250 B.C.), producing
a wedge between western and eastern Greeks. The
only dated record of the Indo-Bactrian king,
Menander (150 B.C.), is purely Indian in style.

By about 150 B.C., direct contact between India
and Greater Greece which included Babylon had almost
ceased, due to the growth of the Parthian empire.
Whatever ideas came, was through the Saka-Kusana
kingdoms which came into existence after 90 B. C. By
that time, astronomy was regarded as only secondary
to planetary and horoscopic astrology, which had
grown to mighty proportions in the West. This may
have been probably one of the main reasons for late
acceptance of Graeco-Chaldean astronomy in India,
for Indian thought during these years ivas definitely
hostile to astrology.

It will surprise many of our readers to be told
that astrology was not liked by Indian leaders of
thought, which dominated Indian life during the period
500 B.C.- 1 A. D. Nevertheless, it is a very correct
view.

The Great Buddha, Whose thoughts and ideas
dominated India from 500 B.C. to the early centuries
of the Christian era, was a determined foe of astro-
logy. In Buddha's time, and for hundreds of years
after Buddha, there was in India no elaborate planetary
or horoscopic astrology, but a crude kind of astrology
based on conjunctions of the moon with stars and
on various kinds of omina such as appearance
of comets, eclipses, etc. But Buddha appears to
have held even such astrological forecasts in great
contempt, as is evident from the following passage
ascribed to him :

Yatha va pan'eke bhonto, Samana-brahmana
saddha-deyyani bhoianani bhurijitva te evarupaya
tiracchana-vijjaya micchajivena-jibdkam kappenti-

seyyathidam "canda-ggaho bhavissati,
suriyaggaho bhavissati, nakkhatta-ggaho bhavissati.
Candima suriyanarh pathagamanarh bhavissati,
candima suriyanarh uppathagamanarh, bhavissati,
nakkhattanam pathagamanam bhavissati,
nakkhattanam uppathagamanarh bhavissati.
Ukkapato bhavissati. Disa-daho bhavissati.
Bhiimicalo bhavissati. Devadundubhi bhavissati.
Candima suriya nakkhattanam uggamanam
ogamajaam samkilesarh vodanam bhavissati."*

(Digha Nikaya, Vol. 1, p. 68, Pali Text Book Society)

Translation : Some brahmanas and §ramatyas earn
their livelihood by taking to beastly professions and
eating food brought to them out of fear ; they say :
"there will be a solar eclipse, a lunar eclipse, occulta-
tion of the stars, the sun and the moon will move in
the correct direction, in the incorrect direction, the
naksatras will move in the correct path, in the
incorrect path, there will be precipitation of
meteors, burning of the cardinal directions (?), earth-
quakes, roar of heavenly war drums, the sun, the
moon, and the stars will rise and set wrongly producing
wide distress amongst all beings, etc."

This attitude to astrology and astrolatry on the
part of Indian leaders of thought during the period of
500 B.C. to 100 A.D., was undoubtedly a correct one,
and would be welcomed by rationalists of all ages and
countries. But such ideas had apparently a very
deterrent effect on the study of astronomy in India.
Pursuit of astronomical knowledge was confused with
astrology, and its cultivation was definitely forbidden
in the thousands of monasteries which sprang all over
the country within few hundred years of the Nirv5na
(544 B.C./ 483 B.C). Yet monasteries were exactly the
places where astronomical studies could be quietly
pursued and monks were, on account of their leisure
and temparament, eminently fitted for taking up such
studies, as had happened later in Europe, where some
of the most eminent astronomers came from the
monkist ranks, e.g., Copernicus and Fabricius.

Neither did Hindu leaders, opposed to Buddhism,
encourage astrology and astrolatry. The practical
politician thought that the practice of astrology was
not conducive to the exercise of personal initiative
and condemned it in no uncertain terms. In the
Arthasa&tra of Kautilya, a treatise on statecraft, which
took shape between 300 B.C. and 100 A.D., and is
ascribed to Canakya, the following passage is
found :

* Acknowledgement is due to Prof. Mm. Bidhusekhar Sastri,.
who supplied these passages.

C. B. — 38

236

REPORT OF THE CALENDAR REFORM COMMITTEE

Kautiliya Artha&astra

Nakflatram atiprcchantam balam artho'tivartate
Arfcho hyarthasya nakaatram kirii karisyanti tarakab.

Translation : The objective (artha) eludes the
foolish man {balam) who enquires too much from the
stars. The objective should be the naksatra of the
objective, of what avail are the stars ?

This may be taken to represent the views of the
practical politician about astrology and astrolatry,
during the period 500 B.C. to 100 B.C.

Canakya was the great minister of Candragupta,
and history says that these two great leaders rolled
back the hordes of the Macedonians, who had con-
quered the Acheminid Empire of Iran comprising
the whole of the Near East to the borders of Iran,
and thereafter laid the foundation of the greatest
empire India has ever seen. They clearly not only did
not believe in astrology, but openly, and uithout reserve,
ridiculed its pretensions.

But the influence of original Buddhism waned after
the rise of Mahayanist Buddhism, which received
great encouragement during the reign of Kaniska
<78 A.D. to 102 A,D.) and other Kusana and Saka
kings. Then came Buddhist iconography, coins, and
knowledge of the methods of western date-recording
which the Sakas and Kusanas used. They blended
with the indigenous Indian system slowly.

The focus of diffusion of western astronomical
knowledge appears to have been the city of UjjayinI,
capital of the western Satraps who were apparently
the first to use a continuous era ( the Saka era ), and
a method of date-recording which was at first purely
Graeco-Chaldean as prevalent in Seleucid Babylon,
but gradually Indian elements like the tithi and the
naksatra were blended, as we find for the first time
in the inscription of Satrap Rudrasimha, dated 181
A.D. t (vide§5-5).

This city of Ujjayini was later adopted as the
Indian Greenwich, for the measurement of longitudes
of places. The borrowal of astronomical knowledge was
not therefore from Greece direct, but as now becomes
increasingly clearer, from the West, which included
Seleucid Babylon, and probably through Arsacid
Persia. The language of culture in these regions
was Greek, and we therefore find Greek words like
kendra (centre), lipiikd (lepton), hora (hour) in use by
Indian astronomers.

This view is supported by the Indian myth that
astrolatry and astrology were brought to India by a
party of Sakadvipi Brahmanas (Scythian Brahmins),
who were invited to come to India for curing Samba,
the son of Krsna, of leprosy by means of incantations

to the Sungod. Professional astrologers, in many
parts of India, admit to being descendants of these
&ahadvipi Brahmanas and probably many of the
eminent astronomers like Aryabhata and Varahamihira
who made great scientfic contributions to astronomy
belonged to this race. The planetary Sungod is always
shown with high boots on, as in the case of Central
Asian kings (e.g., Kaniska).

It is a task for the historian to trace how the steps
in which the importation of western astronomical
knowledge took place for the Siddhantas, which
incorporate this knowledge and are all a few centuries
later, and many of them bear no date.

A good point d y appui for discussion is Varahamihira's
Pa%ca Siddhantikd ; for Varahamihira's date is known.
He died in 587 A.D., in ripe old age so he must have
written his book about 550 A.D. This is a compendium
reviewing the knowledge contained in the five
Siddhantas which were current at his time. These
were regarded as 'Apauruseyd or "knowledge revealed
by gods or mythical persons".

The five Siddhantas are :

Paitarnaha ♦••Ascribed to Grandfather Brahma.

Vasistha •••Ascribed to the mythical sage
Vasistha, a Vedic patriarch, and
revealed by him to one Mandavya.

Romaka •••Revealed by god Visnu to Rsi Romasa
or Romaka.

Paulisa •••Ascribed sometimes to the sage
Pulastya, one of the seven seers or
patriarchs forming the Great Bear
constellation of stars (but see later).

Surya -Revealed by the Sungod to A sura
Maya, architect of gods, who
propounds them to the Rsis.

The five Siddhantas are given in the increasing
order of their accuracy according to Varahamihira.
Thus Varahamihira considers the Surya Siddhanta as
the most accurate, and next in order are the Paulisa,
and the Romaka. The Vasistha and Paitarnaha arc,
according to Varahamihira, not accurate.

Why were those Siddhantas regarded as *' Apauru-
seya" (i.e. not due to any mortal man) ? Dlksit says
{Bharatiya Jyotisdstra, Part II r Chap. 1) :

"The knowledge of astronomy as seen developed
during the Vedic and Vedanga Jyotisa periods and
described in Part I, was wide as compared with the
length of the period ; but it is very meagre, when com-
pared with the present position***. The oldest of
astronomical knowledge (given in the oldest Siddhantas)
reveal a sudden rise in the standard of astronomical
knowledge. Those who raised the standard as given

INDIAN CALENDAR

237

in these works, were naturally regarded as superhuman
and hence the available ancient works on astronomy
are regarded as 'apawuseyd (i.e. not compiled by
mortal men) and it is clear that the belief has been
formed later".

This statement, made by Dlksit nearly sixty years
ago, really singles out only one phase of the issue, viz.,
the wide gulf in the level of astronomical knowledge of
the Siddhantas and that in the Veddnga Jyotisa ;
but leaves the question of actual authorship open. In
our opinion the Siddhantas were regarded as
Apauruseya because they appear to have been com-
pilations by different schools of the knowledge of
calendaric astronomy, as they diffused from the West
during the period 100 B.C.— 400 A.D. But let us look
into them a little more closely.

The Paitamaha Siddhanta : described in five
stanzas in Chap. XII. of the Paftea Siddhantika*

As already discussed it is a revised edition of the
Veddiiga Jyotisa ,but later authors say that it contained
rules for the calculation of motions of the sun, the
moon and also the planets which were not given by
the Veddiiga Jyoli$a. As the full text of the original
Siddhanta has not been recovered, it is difficult to say
how the borrowal took place.

The Vasistha Siddhanta : as known to Varahamihira
is described in 13 couplets in Chap. II of the Pa%ca
Siddhantika. It describes methods of calculating tithi
and nak?aira, which are inaccurate. Besides it mentions
liasi (zodiacal signs), angular measurements, discusses
length of the day, and the lagna (ascendant part of the
zodiac). Apparently this represents one attempt by a
school to propagate western astronomical knowledge.
The school persisted and we have Vddsiha Siddhantas
later than Varahamihira. One of the most famous was
Visnucandra (who was somewhat later than Aryabhata)
who was conscious of the phenomenon of precession
of the equinoxes. No text of the Siddhanta is
available, except some quotations.

Varahamihira pays a formal courtesy to Paitamaha
and VasiMa; this does not prevent him from
describing these two as ' duravibhrasiau\ i.e., furthest
from truth.

The Romaka Siddhanta :

The Bomaka Siddhanta as reviewed by Varahamihira
uses :

A Yuga of 2850 years -19 x 5 x 30 years ;
150 years = 54787 days ;
1 year =365.2467 days.

The number of intercalary months in the yuga is
given as 1050, i.e., there are 7 intercalary months in
19 years.

We need not go any further into the contents of
this Siddhanta. As the name indicates, the knowledge
was borrowed from the West, which was vaguely
known as 'Romaka* after the first century A.D. The
yttga taken is quite un-Indian, but appears to be a
blending of the nineteen-year cycle of Babylon, the
five-yearly yuga of Veddiiga Jyoti§a, and the number 30
which is the number of tithis in a month. The length
of the year is identical with Hipparchos's (365.2467),
and this alone of the Siddhantas gives a length of the
year which is unmistakeably tropical.

The Romaka Siddhanta appears to represent a
distinct school who tried to propagate western astro-
nomical knowledge on the lines of Hipparchos. One
of the later propounders was Srisena, who flourished
between Aryabhata and Brahmagupta ; the latter
ridicules him roundly for having made a "kantha", i.e.
a wrapper made out of discarded rags of all types —
meaning probably Srlsena's attempt to blend two
incongruous systems of knowledge, western and
eastern.

The Paulisa Siddhanta :

This Siddhanta was at one time regarded as the
rival of the Surya Siddhanta, but no text is available
now. But it continued to be current up to the time
of Bhattotpala (966 A.D.), who quotes from it.

Alberuni (1030-44 A.D.) who was acquainted with
it, said that it was an adaptation from an astronomical
treatise of Paulus of Sainthra, i.c, of Alexandria. But
it is not clear whether he had actually seen Paulus's
treatise, and compared it with the Paulisa Siddhanta
or simply made a guess on the analogy of names merely.
The name of one Paulus is found in the Alexandrian
list of savants (378 A.D.) but his only known work is
one on astrology, and it has nothing in common with
Paulisa Siddhanta, which appears to have been purely
an astronomical treatise as we can reconstruct it from
the PaTtca Siddhantika (vide infra). The ascription to
Paulus of Alexandria is not therefore proved. There
is, however, reference in the Pau'isa Siddhanta to
Alexandria, or Yavanapura, as it was known to Hindu
savants. The longitudes of Ujjaini and Banaras are
given with reference to Alexandria (P. S., Chap. III).

The Pa%ca Siddhantika devotes a few stanzas of
Chaps. I, III, VI, VII, and VIII to this exposition of the
Paulisa Siddhanta. Nobody seems to have gone critically
into the contends of these chapters after Dr. Thibaut
who tried to explain these in his introduction to the
Paftca Siddhantika, but left most of them unexplained
owing to their obscurity.

In Chap. I, (verses 24—25), 30 Lords of the days of
the month are mentioned. This is quite un-Indian

238

REPORT OF THE CALENDAR REFORM COMMITTEE

and reminds one of the Iranian calendar in which each
one of thirty days of the month is named after a god
or principle (see § 2.3). The names of the lords of the
days as given in the Paulisa Siddhanta are of course
all Indian.

The Surya Siddhanta

Of all the Siddhantas mentioned by Varahamihira
this alone has survived and is still regarded with
veneration by Indian astrologers. This Siddhanta was
published with annotations by Rev. E. Burgess, in 1860,
and has been republished by the Calcutta University
under the editorship of P. L. Gangooly, with an intro-
duction by Prof. P. C. Sengupta.

This is supposed to have been described by the
Sungod to Asura Maya, the architect of the gods, who
revealed it to the Indian Rsis. These legends certainly
represent some sort of borrowing from the West, but
it would be fruitless to define its exact nature unless
the text is more critically examined. Varahamihira
describes in Chapters IX, X, XI, XVI, XVII of the
Paftca Siddhantika the contents of the Surya Siddhanta
as known to him ; they are somewhat different from
those as found in the modern text. It appears that
this Siddhanta was constantly revised with respect to
the astronomical constants contained in it as all
astronomical treatises should be. The text as we
have now was fixed up by Ranganatha in 1603 after
which there have been no changes. Burgess, from
a study of the astronomical constants, thought that
the final text referred to the year 1091 A.D. Prof.
P. C. Sengupta shows that the S.S. as reported by
Varahamihira borrowed elements of astronomical data
from Aryabhata, and the S.S. as current now has
borrowed elements from Brahmagupta (628 A.D.).

The modern Surya Siddhanta is a book of 500
verses divided into 14 chapters, contents of which are
described briefly below :

Chap. I — Mean motions of the Planets.
n II— True places of the Planets.

Ill— Direction, Place, and Time.
n IV — Eclipses, and especially Lunar
Eclipses.
V— Parallax in a Solar Eclipse.
n VI — Projection of Eclipses.

VII — Planetary Conjunctions.

VIII— The Asterisms.

IX— Heliacal Risings and Settings.

X — Moon's Risings -and Settings, and

the Elevation of her Cusps.

XI — Certain malignant Aspects of the

Sun and the Mocn-.

Chap. XII— Cosmogony, Geography, Dimension
of the Creation.
„ XIII— Armillary Sphere, and other
Instruments.
XIV— Different modes of reckoning Time.

A scrutiny of the text shows that it is, with the
exception of a few elements, almost completely astro-
nomical. A few verses in Chap. Ill, viz., Nos. 9-12
deal with the trepidation theory of the precession of
equinoxes. These are regarded by all critics of the
Surya Siddhanta to be interpolations made after the
12th century.

It will take us too much away from bur main theme
to give a critical account of this treatise, but every
critic has admitted that the text does not show any
influence of Ptolemy's Almagest. Prof. P. C. Sen-
gupta's introduction is particularly valuable. This
Siddhanta indicates that longitudes should be calculated
from Ujjain and makes no mention of Alexandria.
Prof. Sengupta thinks that it dated from about 400
A.D., but a scrutiny of the co-ordinates of certain stars
marking the ecliptic, which we have discussed in
Appendix 5-B, shows that it might have utilized data
collected about 280 A.D., when the star Citra
(a Virginia), was close to the autumnal equinoctial
point, and is therefore subsequent to 280 A.D.

The rules of framing the calendar are found in
Chapter XII of which we give an account in the next
section.

After about 500 A.D., the Indian astronomers gave
up the pretext of ascribing astronomical treatises to
gods or mythical sages and began to claim authorship
of the treatises they had written ; the earliest that has
survived is that of Aryabhata (476— 523 A.D.). The
objects of their treatises were to frame rules for
calendaric calculations, knowledge of astronomy
forming the basis on which these rules were
framed.

In addition to the Surya Siddhanta only two other
systems have survived, viz-,

The Arya Siddhanta- due to Aryabhata II, an
astronomer of the 10th century,_and supposed to be
related to the Aryabhatiya of Aryabhata, who claims
to have derived it from Brahma, the Creator.

The Brahma Siddhanta— vaguely related to the
Paitamaha Siddtenta, but the human authorship is
ascribed to the celebrated astronomer Brahmagupta
(628 A.D.).

But a number of astronomical treatises like that of
Siddhanta kirormni by Bhaskaracarya and many
others, have survived either on account of their own
merit or their connection with astrology.

INDIAN CALENDAR

239

The Solar Calendar according to the
Surya Siddhanta

The first few verses of Chap. XII deal with the
creation of the world according, to Hindu conception,
and the creation of the elements ; of the sun, the
moon, and the planets. The universe is taken to be
geocentric, and the planets in order of their decreasing
distances from the earth are given as (vide verse 3 J,) :
Saturn, Jupiter, Mars, the Sun, Venus, Mercury
and the Moon.
The fixed stars are placed beyond the orbit of Saturn.

Surya Siddhania> XII, Verse 32
Mauhye samantat dandasya bhugolo byomni tisthati
Bibhranati paramam sakfcim brahmarto dharanatmikaiii.

Translation : Quite in the middle of the celestial
egg (Brahmano)a\ the earth sphere (Bhugola) stands in
the ether, bearing the supreme might of Brahma
which has the nature of a self supporting force.

The astronomers are thus conscious that the earth
is a spherical body suspended in ether {byomni)

Verse 34 : Describes the earth's polar axis, which
passing through the earth's centre emerges as
mountains of gold on either side.

Verse 35 : Gods and Rsis are supposed to dwell
on the upper (northern) pole, and the demons are
supposed to dwell on the nether (south) pole.

Verse 43 : Describes two pole-stars (Dhruva*taras)
which are fixed in the sky.

The author could have been aware only of the
Polaris. By analogy he inferred the existence of a
southern pole-star which, as is well-known, does
not exist. He had apparently no knowledge of the sky
far south of the equator.

The remaining verses describe the equator : As in
modern astronomy, it says that the polar star is on the
horizon of a person on the equator and the co-latitude
(Lambaka) of the equator is 90°.

The Siddhantic astronomers thus completely
accepted the geocentric theory of the solar system. It
was a great improvement on the ideas of the world
prevalent in India at the time of the great epic
Mahabharata (date about 300 B.C.), in which the earth
is described to be a flat disc, with the Sumeru
mountain as a protruding peg in the centre, round
which the diurnal motion of the celestial globe carrying
the stars, planets, the sun and the moon takes place.
This idea of the world is also found in the Jatakas and
other Buddhist scriptures.

In the subsequent verses four cardinal points on the
equator are recognized, these are :

Lanka, which is technically the name of a locality
on the equator lying in the meridian of Ujjayini, which
was the Greenwich of ancient India. This Lanka had
nothing to do with Ceylon, but is a fictitious name ;

90° west of Lanka the city called Romaka, and
90° east of Lanka the city known as Yamakoti.

The name Romaka vaguely refers to the capital of
the Roman Empire. ' Yamakoti' is quite fanciful.

The Surya Siddhanta takes it for granted that the
sun's yearly motion through the ecliptic is known to
the reader and now proceeds to explain the Signs of
the Zodiac.

Surya Siddhanta XII, 45

Mesadau devabhagasthe devanarii yati darsanam
Asuranam tuladau tu suryastadbhaga saficarah.

Translation : In the half revolution beginning
with Mesadi (lit. the initial point of Aries), the sun
being in the hemisphere of gods, is visible to the gods, ;
but while in that beginning with Tuladi (lit. the initial
point of Libra) he is visible to the demons moving in
their hemesphere.

This means that when the sun reaches Mesadi, the
initial point of the sign of Aries, the gods who are
supposed to be in the north pole just witness the
rising of the sun and has the sun over the horizon for
six months. All these six months, the demons who are
supposed to be at the south pole are in the dark. It
is vice versa for their enemies the Asuras for whom,
dwelling in the south pole, the sun rises for them
when it is at Tuladi (beginning of the Tula sign i.e.,
first point of Libra) and remains above the horizon for
six months.

According to the S.S., therefore, the first point of
Aries is coincident with the vernal equinoctial point, and
the first point of Libra tuith the auturtinal equinoctial
point.

Surya Siddhanta, XIV, 9 and 10

Bhanormakarasamkranteb sanmasa uttarayanarii
Karkadestu tathaiva syat sanmasa daks in ay ana m. 9 ,
Dvirasinatha rtava stato'pi sisiradayat
Mesadayo dvadasaite masastaireva vatsarah. 10,

Translation: From the moment of the sun's entrance
(safnkrdnti) into Makara, the sign of Capricorn, six
months make up his northward progress (uttarayana) ;
so likewise from the moment of entrance into Karkata,
the sign of Cancer, six months are his southward
progress (daksinayana). (9)

Thence also are reckoned the seasons (rtu), the
cool season (siUra) and the r£st, each prevailing
through two signs. These twelve, commencing with

240

REPOBT OF THE CALENDAR REFORM COMMITTEE

Aries, are the months ; of them is made up tke
year (10).

These quotations leave not the slightest doubt that
according to the compilers of the S.S., the first point
of the zodiac is the point of intersection of the ecliptic
and the equator, and the signs of the zodiac cover 30°
each of the ecliptic.

It is supposed on good grounds that much of the
astronomical knowledge found in the Surya Siddhanta
is derived from Graeco-Chaldean sources. But it is
clear from the text that the compilers of the S.S. had
no knowledge of the precession of equinoxes, but they
took the first point of Aries to be fixed. This is not to
be wondered at, for as shown in § 4.9, inspite of the
works of Hipparchos and Ptolemy, precession was
either not accepted or no importance was attached to
it by the astronomers of the Roman empire. It may be
added that the compilers of the S.S. were not aware
of the theory of trepidation of equinoxes which
appears to have been first formulated in the West by
Theon of Alexandria (ca. 370 A.D.). It is also important
to note that the Indian astronomers did not take the
first point of Aries to be identical with that given
either by Hipparchos, Ptolemy or any other western
authority as would have been the case if there was
blind-folded borrowing. They assimilated the astro-
nomical knowledge intelligently and took the first
point of Aries as the point of intersection of the
equator and the ecliptic, and made successive attempts
to determine it by some kind of actual observations,
as shown in appendix 5-B. These observations appear
first to have been made about 280 A.D.

Length of the Year

The length of the year, according to the different
authorities are as follows,

Surya Siddhanta of days

Varahamihira ... 365 d 6 U 12- 36" =365.25875

Current S.S. ... 365 6 12 36.56 = 365.258756

Ptolemy (sidereal) 365 6 9 48.6 = 365.256813
Correct length of

the sidereal year. .. 365 6 9 9.7 = 365.256362
Correct length of

the tropical year- 365 5 48 45.7 = 365.242196

N. B. Varahamihira's length of the year is also found in
Aryabhata's ardhardtrika, or midnight system, and in
Brahmagupta's Khari^ix Khadyaka.

How did the. Indian savants manage to have such a
wrong value for the length of the year ?

The year, according to the Surya Siddh&nta, is
meant to be clearly tropical, but as the Indian savants
compiling the S.S. were ignorant of the phenomenon of

precession of the equinoxes, they were unaware of the
distinction^ between the sidereal year and the tropical
year. They had to obtain the year-length either from
observation or from outside sources. If they obtained
it from observations, they must have counted the
number of days passed between the return of the sun
to the same point in the sky over a number of years.
Such observations would show that the year had not
the traditional value of 366 days given in Vedanga
Jyotisa, but somewhat less. In fact, the Paitamaha
length is 365.3569 days and there is no reason to
believe that it was derived from foreign sources.
Successive observations must have enabled the Indian
savants to push the accuracy still higher.

Or alternatively they might have borrowed the
value from Graeco-Chaldean astronomy, but we cannot
then explain why their value is larger than Ptolemy's.
We have seen that the Romaka Siddhanta gives a value
which is Hipparchos's, and tropical, but the three more
correct SiddhSntas reject it, as being too small. This
however indicates that they probably tried to derive
the length from observations as stated in the previous
paragraph and found the Romaka SiddhantaAength. too
small. If they had taken it from some other source,
we have still to discover that source. It is certainly
not Ptolemy's Almagest

The ex-cathedra style of writing adopted by the
Siddhantic astronomers, e.g., the number of days in a
Kalpa (a period of 4.32 x 10* years) is 1,577,917,828,000
according to Grandfather Brahma, or the Sungod,
does not enable one to trace the steps by which these
conclusions were reached.

The two problems of (i) distinguishing between the
tropical year, and the sidereal year and of (ii) deter-
mining the correct length of the year in terms of
the mean solar days are very exacting ones.

We have seen how it took the West the whole
time-period between 3000 B.C. to 1582 A.D. to arrive
at the idea that the true length of the tropical year
was close to 365.2425 days. Probably Iranian astrono-
mers of Omar Khayam's time (1072 A.D.), who had the
advantage of the great Arabian observations by al-
Battanl and others had a more correct knowledge of
this length. The final acceptance of the distinction
between the tropical and the sidereal year dates only
from 1687 A.D., when Newton proved the theory of
trepidation to be wrong.

The Siddhantic astronomers of 500-900 A.D. cannot
therefore be blamed for their failure to grasp the two
problems. But what to say of their blind followers
who, in the twentieth century, would continue to
proclaim their belief in the theory of trepidation ?

INDIAN CALENDAB

241

Effect of continuance of the mistake

The Surya Siddh&nta value, vix. t 365.258756 days is
larger than the correct sidereal value by "002394 days
and larger than the tropical length by .016560 days.

As the S.S. value is still used in almanac-framing,
the effect has been that the year-beginning is advancing
>y .01656 days per year, so that in course of nearly 1400
years, the year-beginning has advanced by 23.2 days,
so that the Indian solar year, instead of starting on the
day after the vernal equinox (March 22) now starts on
April 13th or 14th. The situation is the same as
happened in Europe, where owing to the use of a
year-length of 365.25 days, since the time of Julius
Caesar, the Christmas preceded the winter solstice by
10 days, when the error was rectified by a Bull of
Gregory XIII, and the calendar was stabilized by
introducing revised leap-year rules.

The Calendar Reform Committee has proposed that
the Indian New Year should start on the day after the
vernal equinox day. Most of the Indian calendar
makers belong to the no-changer school, or the
nirayana school (i.e., school not believing in the
precession of the equinoxes). But this school does
not realize that even if the sidereal length of the year
be acceped, the Indian year-length used by them is
larger by nearly '0024 days, which cannot be tolerated.
So if a change has to be made, it is better to do it
whole -hog, i.e., take the year-length to be tropical, and
start the year on the day after the vernal equinox.

This is the proposal of the Indian Calendar Reform
Committee, and it is in full agreement with the canons
laid down in the Surya Siddhanta.

Historical Note on the Year-beginning

The Indian year, throughout ages, has been of two
kinds, the solar and the lunar, each having its own
starting day- The year-beginning for the two kinds
of years, for different eras* is shown in Table No. 27.

The Starting Day of the Solar Year

In the Vedic age, the year-beginning was related
probably to one of the cardinal days of the year, but
we do not know which cardinal day it was. The
Ved&iiga Jyotisa started the year from the winter
solstice day, Brdhmaws started the year from the
Indian Spring (Vasanta) when the tropical (Say ana)
longitude of the sun amounted to 330°.

The Siddhantic astronomers must have found a
confusion, and so fixed up a rule for fixing the year-
beginning, which we have just now dicussed. These
rules amount to :

(a) Starting the astronomical year from the
moment the sun crosses the vernal equinoctial point.

(b) Starting the civil year on the day following.

The Siddhantic astronomers thus brought the
Indian calendar on a line with the Graeco-Chaldean
calendar prevalent in the Near East during the
Seleucid times.

In a few cases, e.g., in the case of the Vikrama
era reckoning as followed in parts of Guzrat, the year-
beginning is in Kartika. This seems to be reminiscent
of the custom amongst the Macedonian Greek rulers
of Babylon to* start the year on the autumnal equinox
day.

The First Month of the Year :

This has to be defined with respect to the defini-
tion of the seasons.

According to modern convention, which is derived
from Graeco-Chaldean sources, the first season of the
year is spring ; it begins on the day of vernal equinox,
as shown in fig. 25 which shows also the other seasons.
The Indian classification of seasons is, however,
different as the following table shows.

Table 15 — Indian Seasons.

— 30° to 30°... Spring (Vasanta) Caitra & Vaisakha
30 to 90 . . .Summer (Grisma) Jyaistha & A^iidha
90 to 150 ...Rains (Varsa) ^ Sravana & Bhadra
150 to 210 ...Early Autumn (Sarat) Asvina & Kartika
210 to 270 ...Late Autumn Agrahayana & Pausa

(Hemanta)

270 to 330 ...Winter (Sisira) Magna & Phalguna

The Siddhantic astronomers, therefore, found
themselves in a difficulty. If they were to follow 'the
Indian convention, Caitra would be the first month
of the solar year. If they were to follow tfie Graeco-
Chaldean covention, they had to take VaUakha as
the first month of the solar year.

They struck a compromise. For defining the solar
year, they took Vaisakha as the first month and for
defining the lunar year they took Caitra as the first
month (see § 5*7).

But this rule has been followed only in North
India. In South India, they had different practices,
as shown in the list of solar month -names (Table
No. 16).

In North India the first month is Vaisakha as
laid down in the S.S. which starts just after sun's
passage through the V.E. point.

It is interesting to see that in Tamil Nad, some of
the names are of Sanskritic origin, others are of Tamil
origin. But the most striking fact is that the first mouth,
starting after vernal equinox is not Vaisakha as in the

242

BEPOKT OF THE CALENDAR REFORK COMMITTEE

Table 16.

Indian Names
of Signs

Corresponding Names of Solar Months.

Bengal
Orissa

Assam

Tamil

Tinnevelly
or S. Malayalam
(Orissa)

N. Malayalam

VAISAKHA

BAHAG

CITTIRAI

MESA

MEDAM

Vrsava

Jyaistha

Jeth

Vaikasi

Vrsava

Edavam

Mithuna

A s^dha

Ahar

Ani

Mithuna

Midhunam

Karkata

Sravana

Saon

Adi

Karkitaka

Karki$aka

Siriiha

Bbadra

Bhad

Avani

SIMHA

Cingam

Kanya

Asvina

Ahin

Pura^tasi

Kanya

KANNI

Tula

Kartika

Kati

Arppisi (Aippasi)

Thula

Thulam

Vrscika

Agrahayana

Aghon

Karthigai

Vrscika

Vrscikam

Dhanul.i

Pausa

Puha

Margali

Dhanug

Dhanu

Makara

Magha

Magh

Thai

Makara

Makaram

Kumbha

Phalguna

Phagun

Masi

Kumbha

Kumbham

Mina

Caitra

Ca'fc

Panguni

Mina

Minam

(The first month of the year has been distinguished by capitals).

taken without change from Sanskrit. The Assamese

N.B. The Bengali or Oriya names of solar months are
names are the same, but have local pronunciations.

rest of India but Ghittirai or Caitra, and so on. We do
not know why Tamil astronomers adopted a different
convention. We can onlv guess : probably they wanted
to continue the old Indian usage that Caitra is to
remain the first month of the year.

In Tinnevelley and Malayalam districts the solar
months are named after the signs of the zodiac.

There is, therefore, no uniformity of practice in the
nomenclature of the solar months, and in fixing up
the name of the first month of the solar year.

Solar Months : Definition

After having defined the solar year, and the year
beginning, the Surya Siddhanta proceeds to define the
"Solar Month."

Surya Siddhanta, Chap. 1,13

Aindavastithibhi-stadvat samkrantya saura ucyate
Masairdvadasabhirvarsarii divyam tadaharucyate.

Translation : A lunar month, of as many lunar
days, (fithi) ; a solar (saura) month is det2rmined by
the entrance of the sun into a sign of the zodiac, i.e.
the length of the month is the time taken by the sun
in passing 30° of its orbit, beginning from the
initial point of a sign ; twelve months make a year,
this is called a day of the gods.

This definiton is accepted by the Arya, and
Brahma Siddhantas as well.

The working of this rule gives rise to plenty of
difficulties, which are described below :

The mean length of a solar month

-30.43823 according to S.S.

=* 30.43685 according to modern data.

The actual lengths of the different solar months*
however, differ widely from the above mean values.
This is due to the fact that the earth does not move
with uniform motion in a circular orbit round the sun,
but moves in an elliptic orbit, one focus of which is
occupied by the sun, and according to Kepler's second
law, it sweeps over equal areas round the sun in equal
intervals of time. When the earth is farthest from
the sun, i.e. at aphelion (sun at apogee) of the
elliptic orbit, the actual velocity of the earth becomes
slowest, and the apparent angular velocity of the
sun becomes minimum, and consequently the length
of the solar month is greatest. This happens about
3rd or 4th July, i.e., about the middle of the solar
month of Asadha (Mithuna), and consequently this
month has got the greatest length. The circumsfances
become reversed six months later on about 2nd or 3rd
January, when the earth is nearest to the sun, i.e., at
perihelion (sun at perigee), the angular velocity of the
sun at that time becomes maximum, and consequently
the solar month of Pausa (Dhanufy) which is
opposite to Ssadha, has got the minimum length.
The following two figures ( Nos. 25 & 26 ) will explain
the position.

The durations of the different months, which are
different from each other due to the above reason, are
also not fixed for all time. The durations of the solar

INDIAN CALEN DAB

243

months undergo gradual variations on account of two
reasons ; v%%.$

(i.e.

Fig. 25

(i) the line of apsides of the earth's elliptic orbit
the aphelion and perihelion points) is not fixed

Fig. 26

in space but is advancing along the ecliptic at the
rate of 61".89 per year or l.°72 per century. This is

Table 17 — Lengths of different solar

made up of the precessional velocity of 50. "27 per year
in the retrograde direction and the perihelion velocity
of 11. "62 per year in the direct direction due to
planetary attraction. This movement of the apse line
with respect to the V.E. point causes variation in the
lengths of the different months.

(ii) The second reason is that the ellipticity
of the earth's orbit is not constant ; it is gradually
changing. At present the eccentricity of the orbit is
diminishing and the elliptic orbit is tending to become
circular. As a result, the greatest duration of the
month is diminishing in length and the least one
increasing. Similarly the lengths of other months are
also undergoing variation.

The modern elliptic theory of planetary orbits was
not known to the makers of Indian Siddhantas, but
they knew that the sun's true motion was far
from uniform. They conceived that the sun has
uniform motion in a circle, with the earth not
exactly at the centre of that circle, but at a
small distance from it. The orbit therefore becomes-
an eccentric circle or an epicycle. Here also the
angular motion of the sun becomes minimum when at
apogee or farthest from the earth, and maximum when
nearest to the eartn or at perigee. In this case the
size and eccentricity of the circle are invariable
quantities, and consequently the maximum and
minimum limits of the months are constant. The
apse line advances in this case also, but with a very
slow motion, which according to the Surya Siddhanta
amounts to a degree of arc in 31,008 years, or 11" in a
century. The variations of the durations of months
due to this slow motion of the apse line is quite
negligible and the lengths of the months according to
the Surya Siddhanta are practically constant over ages.

months reckoned from the vernal equinox.

Lengths of Solar months.

According to

Modern value

SUrya Siddhanta

(1950 A.DJ

{as proposed)

(1)

(2)

(3)

(4)

(5)

Vaisakha (Me$a)

( o c

J -30° )

26.8

25.2

Caitra

Jyais^ha (Vftfa)

( 30

-60 )

5.2

29.6

Vaisakha

A$adha (Mithuna)

( 60

-90 )

28.4

101

Jyaistha

t^ravana (Karka^a)

( 90

-120 )

24.4

54.6

A sad ha

Bhadra (Simha)

(120

-150 )

26.8

53.1

J^ravana

Asvina (Kanya)

(150

-180 )

35.6

18.7

Bhadra

Kartika (Tula)

(180

-210 )

26.4

58.2

Asvina

Agrahayana (Vrscika)

(210

-240 )

46.0

14.6

Kartika

Pausa (Dh&nub)

(240

-270 )

37.6

8.7

Agrahayana

Magna (Makara)

(270

-300 )

45.2

38.6

Pauga

Phalguna (Kumbha)

(300

-330 )

41.2

18.5

Magha

Caitra (Mina)

(330

-360 )

29.0

18.9

Phalguna

365

12'6

365

48*8

O.B.— 39

244

REPORT OF THE CALENDAR REFORM COMMITTEE

In the Surya Siddhdnta, a formula is given for
finding the true longitude of the sun from its mean
longitude. As the length of a month is the time taken
by the sun to traverse arcs of 30° each along the
ecliptic by its true motion, the lengths of the different
months can be worked out when its true longitudes on
different dates of the year are known. The true
longitude is obtained by the Surya Siddhdnta with the
help of the following formula :

True Long. — Mean Long. — 133. '68 sin K

+ 3.18 sin 2 K

where K~ Mandakendra of the sun,
i.e., — mean sun — sun's apogee.

Different conventions for fixing up the
beginning of the solar month

The safnkranti or ingress of the sun into the
different signs may take place at any hour of the day.
Astronomically speaking the month starts from that
moment. But for civil purposes, the month should
start from a sunrise ; it should therefore start either
on the day of the safnkranti or the next following
day according to the convention adopted for the
locality. There are four different conventions in
different States of India for determining the beginning
of the civil month.

At the approximate time of each safnkranti, the
true longitude of the sun is calculated by the above
formula for two successive days, one before the
attainment of the desired multiple of 30° of longitude
and the other after it, and then the actual time of
crossing the exact multiple of 30th degree is obtained
by the rule of simple proportion. This is called the
time of safnkranti or solar transit. The time interval
between the two successive safnkrdntis is the actual
length of the month, The lengths of the months thus
derived from the Surya Siddhdnta compared with the
modern values, i.e., the values which we get after
taking the elliptic motion of the sun, and the shift of
the first point of Aries are shown in Table No. 17,
on p. 243, in which : —

Column (1) gives the names of months.

„ (2) gives the arc measured from the first

point of Aries (the V.E. point)
covered by the true longitude
of the sun.

„ (3) gives the lengths of the months

derived from the Surya-
Siddhdnta rules.

(4) gives the correct lengths of the

months as in 1950 A.D.

(5) gives the corresponding names of the

months as proposed by the
Committee.

It would appear from table No. 17 that the
lengths of the months of the Surya Siddhdnta are no
longer correct ; they greatly differ from their corres-
ponding modern values, sometimes by as much as 11 J
hours. The Surya Siddhdnta value s, which the
almanac makers still use, are therefore grossly
incorrect. Moreover, the lengths of the months are
undergoing gradual variation with times due to reasons
already explained.

Rules of Samkranti

The Bengal rule : In Bengal, when a safnkranti
takes place between sunrise and midnight of a civil
day, the solar month begins on the following day ; and
when it occurs after midnight, the month begins on
the next following day, i.e., on the third day. This is
the general rule j but if the safnkranti occurs in the
period between 24 minutes before midnight to 24
minutes after midnight, then the duration of tithi
current at sunrise will have to be examined. If the
tithi at sunrise extends up to the moment of safnkranti,
the month begins on the next day : if the tithi ends
before safnkranti, the month begins on the next
following or the third day. But in case of Karkata
and Makara safnkrdntis, the criterion of tithi is not
to be considered. If the Karkata safnkranti falls in
the above period of 48 minutes about the midnight, the
month begins on the next day, and if the Makara
safnkranti falls in that period, the month begins on the
third day.

The Orissa rule : In Orissa the solar months of the
Amli and Vilayati eras begin civilly on the same day
(sunrise to next sunrise) as the safnkranti, irrespective
of whether this takes place before or after midnight.

The Tamil rule : In the Tamil districts the rule is
that when a safnkranti takes place before sunset, the
month begins on the same day, while if it takes place
after sunset the month begins on the following day.

The Malabar rule : The rule observed in the North
and South Malayalam country is that, if the samkranti
takes place between sunrise and 18 ghatykds (7 h 12 U1 )
or more correctly fth of the duration of day from
sunrise (about 1-12^ P.M.) the month begins on the
same day, otherwise it begins on the following day.

It will be observed that as a result of the different
conventions combined with the incorrect month-
lengths of the Surya Siddhdnta we are faced with the
following problems

INDIAN CAItENDAB

245

(1) the civil day of the solar month-beginning
may differ by 1 to 2 days in different parts of India.

(2) The integral number of days of the different
solar months also vary from 29 to 32.

The months of Kartika, Agrahayatya, Pau§a, Magha
and Phalguna contain 29 or 30 days each, of which
two months must be of 29 days, and others of 30 days.
The months Caitra, Vai&akha and Asvina contain 30
or 31 days.

The • rest, vix., Jyaistha, Asa4ha, Sravana and
Bhadra have got 31 to 32 days each, of which one or
two months will contain 32 days every year.

(3) The length of the month by integral number
of civil days is not fixed, it varies from year to year.

Justification of the Solar Calendar as proposed
by the Committee

It has been shown that the intention of the maker
of Surya Siddhanla and of other Siddhantas was to
start the year from the moment of sun's crossing the
vernal equinoctial point and to start the civil year
from the day following. The Committee has also
adopted this view and proposed that the civil year
for all-India use should start from the day following
the V. E. day, i.e., from March 22. In the Vedic
literature also it is found that the starting of the year
was related with one or other of the cardinal days of
the year. The Vedafiga Jyotisa started the year from
the winter solstice day, the Brahmanas started the
year from the Indian spring (Vasanta) when the
tropical {Sayana) longitude of the sun amounted to
330°, but in the Siddhantic period the year-beginning
coincided with the V.rE. day. So in adopting the
Sayana system in our calendar calculations, the
Indian tradition, from the Vedic times up to the
Siddhantic times, has been very faithfully observed.
This has ensured that the Indian seasons would
occupy permanent places in the calendar.

As regards the number of days per month, although
the Surya Siddhanta defines only the astronomical
solar month as the time taken by the sun to traverse
30° of arc of the ecliptic, four different conventions
have been evolved in different States of India for
determining the first day of the civil month from the
actual time of transit as narrated earlier. None of
the conventions is perfect. Such rules do not yield
fixed number of days for a month, as a result of
which it becomes extremely difficult for a chrono-
logist to locate any given date of this calendar,
unambiguously, in the Gregorian calendar, without
going through lengthy and laborious calculations.
Moreover, the number of days of months obtained

from such rules vary from 29 to 32, which is very
inconvenient from various aspects of civil life.

The Committee has therefore felt that there is no
need for keeping the solar months as astronomically
defined. The length of 30 and 31 days are quite
enough for civil purposes. Moreover, fixed durations
of months by integral number of days is the most
convenient system in calendar making. The five
months from the second to the sixth have the lengths
of over 30| days, and so their lengths have been
rounded to 31 days each ; and to the remaining
months 30 days have been allotted.

5.7 THE LUNAR CALENDAR IN THE SIDDHANTA
JYOTISHA PERIOD

The broad divisions of the year into seasons or
months are obtained by the solar calendar, but since
for religious and social puposes the lunar calendar had
been used in India from the Vedic times, it becomes
incumbent to devise methods for pegging on the lunar
calendar to the solar.

The extent to which the lunar calendar affects
Indian socio-religious life will be apparent from the
tables of holidays we have given on pp. 117-154. There
the religious and social ceremonies and observances
and holidays of all states and communities are classified
under the headings :

(1) Regulated by the solar calendar of the
Siddhantas ;

(2) Regulated by Gregorian dates ;

(3) Regulated by the lunar calendar.

The tables show that by far the largest number of
religious holidays and other important social ceremonies
are regulated by the lunar calendar. It is difficult to
see how the lunar affiliation, inconvenient as it is, can
be replaced altogether, short of a revolution in which
we break entirely with our past. The -lunar calendar
will therefore continue to play a very important part
as we continue to keep Our connection with the past,
and with our cherished traditions.

Let us now restate the problems which arise when,
with reference to India, we want to peg the lunar
calendar to the solar, how it was tackled in the past,
and how the Calendar Reform Committee wants to
tackle it.

The lunar month consists of 29.5306 days and 12
such lunar months fall short of the solar year by 10.88
days. After about 2 or 3 years one additional or inter-
calary lunar month is therefore necessary to make up
the year ; and in 19 years there are 7 such intercalary
months. In Babylon and Greece there were fixed rules

246

BEPOBT OF THE CALENDAB BEFOBM COMMITTEE

for intercalation ; the intercalary months appeared at
stated intervals and were placed at fixed positions in
the calendar (vide § 3.2). It appears that some kind of
rough rules of intercalation of lunar months were
followed in India up to the first or second century
A.D. when the calendar was framed according to
the rules of Vedaiiga Jyoti§a (vide § 5.4). Thereafter
the Siddhantic system of calendar-making began
to develop, replacing the old Vedaiiga calendar.

The Vedaiiga calendar as we have seen was crude
and was based on approximate values of the lunar and
solar periods, the calendar was framed on the mean
motions of the luminaries, and as such an intercalary
month was inserted regularly after every period of
30 months.

The Siddhanta Jyotisa introduced the idea of true
positions of the luminaries as distinct from their mean
positions, and devised rules for framing the calendar
on the basis of the true positions, and adopted more
correct values for the periods of the moon and the
sun. But some time elapsed before new rules were
adopted, and intercalary months continued to be
calculated on the basis of the mean motions of the
sun and the moon, employing however more correct
values of their periods as given by the Siddhantas. In
this connection the following remarks by Sewell and
Dlksit, in the Indian Calendar (p. 27) are worth noting.

"It must be noted with regard to the intercalation and
suppression of months, that whereas at present these are
regulated by the sun's and moon's apparent motion, — in other
words, by the apparent length of the solar and lunar months
— and though this practice has been in use at least from
1100 A.D. and was followed by Bhaskaracaryn, there is
evidence to show that in earlier times they were regulated
by the mean length of months. It was at the time of the
celebrated astronomer Sripati (1039 A.D.) that the change
of practice took place".

Intercalary months or Malamasas.

The length of the Surya Siddhanta year is 365.258756
days and of a lunar month according to the S. S. is
29.5305879 days. Twelve such lunar months fall short
of the S. S. year by 10.891701 days. The lunar year
therefore slides back on the solar scale each year by
about 11 days. If the months were allowed to slide
back continuously it would have completed the cycle
in 33.5355 years, and the festivals attached to the lunar
calendar would have moved through all the seasons
of the year within this period, as now happens with the
Islamic calendar.

To prevent the occurrence of this undesirable
feature, the system of intercalary months or mala m&sas

have been introduced. Taking the mean vaules of the
lunation-period and of the length of the solar year,
the time when one extra month (i.e., intercalary month)
will have to be introduced can easily be determined.
But the luminaries do not move with uniform angular
motions [throughout their period of revolution and so
the determination af the intercalary month on the
basis of the actual movement of the sun and the moon
is a very difficult problem. The calculations according
to the mean motions are however shown below.

Table 18 — Calculation of intercalary months in a

19-year cycle.

Surya
Siddhanta

days

Length of year 365.258756
Solar month 30.438230
Lunation 29.53Q581
No. of solar months

after which a lunar

month is added 32.5355

19 years =
235 lunations
( = 19x12 + 7)

Error in the
19-year cycle

6939.91636
6939.68818

-0.22818

Modern-
Sidereal

days

365.256361
30.438030
29.530588

32.5427
6939.86896

6939.68818
- 0.18078

Modern-
Tropical

days

365.242195
30.436850
29 530588

32.5850
6939.60171

6939.68818
+ 0.08617

It would appear from the above figures that the
19-year cycle with 7 mala masas is a better approxi-
mation if we adopt the tropical year, and the error
gradually increases with the sidereal year and the
Surya Siddhanta year. In Hi cycles, i.e., in 220 years,
the discrepancy would amount to only a day in the
case of the tropical year.

It is also seen that one intercalary month is to be
added at intervals of 32* solar months, or in other
words an intercalary month recurs alternately after 32
and 33 solar months. According to this scheme the
intercalary months in a period of 19 years would be as
follows : —

Year

1
2
3
4
5
6
7
8
9
10

Intercalary month
9 Margaslrsa
5 SrSvana
2 Vaisakha

Year Intercalary month

11 10 Pausa

12 —

13 —

14 7 Ssvina

15 ~

16 —

17 3 Jyestha

18 —

19 12 Phal^^a

INDIAN CALENDAR

247

But the makers of Indian calendars have not
followed any scheme for intercalation based on mean
motions. They evolved a plan for distinguishing an
intercalary month from a normal month based on the
true motions of the sun and the moon. This plan is
also followed in giving the name to a lunar month, as
explained below :

Siddhantic rules for the Lunar Calendar

There are two kinds of lunar months used in India,
the new-moon ending and the full-moon ending. In
calendarical calculations only the new-moon ending
months are used.

(i) The new-moon ending lunar month covers the
period from one new-moon to the next. This is known
as amanta or mukhya candra mdsa. It gets the same
name as the solar month in which the moment of initial
new-moon of the month falls. For this purpose the
solar month is to be reckoned from the exact moment
of one safnkranti of the sun to the moment of the next
safnkranti. When a solar month completely covers
a lunar month, i.e., when there are two moments of
new-moon (amanta), one at the beginning and the other
at the end of a solar month, then the lunar month
beginning from the first new-moon is the intercalary
month, which is then called an adhika or mala masa,
and the lunar month beginning from the second new-
moon is the normal month which is termed as suddha
or nija in the Siddhantic system. Both the months
bear the name of the same solar month but are prefixed
by adhika or suddha as the case may be. In an adhika
month religious observances are not generally allowed.

If on the other hand, a lunar month completely
covers a solar month, no new-moon having occurred
in that solar month, the particular lunar month is then
called a ksaya or decayed month.

As the mukhya or new-moon ending lunar month
begins from the Amavasyd or the new-moon occurring
in the solar month bearing the same name, the lunar
month may begin on any day during that solar month
— it may begin on the first or even on the last day of
that solar month.

(ii) The full-moon ending lunar month known as
purnirnanta or gauna candra masa, covers the period
from one full-moon to the next, and is determined on
the basis of the corresponding new-moon ending month
as defined above. It begins from the moment of full-
moon just a fort-night before the initial new-moon of
an amanta month, and it also takes the name of that
month.

But in the gaunamdna (i.e., full-moon ending lunar
month), as the month starts 15 . days earlier than the

new-moon ending month, it may begin on any day
during the last half of the preceding solar month and
the first half of the solar month in question. It will
therefore be seen that while the new*moon ending or
mukhya month sometimes falls almost entirely out-
side (i.e, % after) the relative solar month, the full-moon
ending or a gauna month always covers at least half of
the solar month' of that name.

The months used for civil purposes in the Hindi
calendar are the full-moon ending lunar months, and
are sub-divided into two halves — kf$na pak$a covering
the period from full-moon to new-moon and termed
as vadi, and sukla paksa covering the period from new-
moon to full-moon and termed as sudi. As these
months are on the gaum mana, the vadi half of a
month comes first followed by the sudi half. The last
day of the year is therefore a full-moon day, the
Phalgunl (or Holi ) Purnima, in keeping with the
ancient Indian custom.

The Samvat and Saka years in the Hindi calendar
begins with Caitra Sukla Pratipad. For astronomical
purposes, however, the year begins a few days later
with the entrance of the sun into Mesa.

The calendars of Asaq^hi Safnvat and Karlikl Safnvat
are, on the other hand, based on the new-moon ending
months, and consequently the months begin 15 days
later than the months of the Caitradi full-moon ending
calendar. The A sa^hl calendar begins with Asa4ha
Sukla 1, and the Kartikl calendar with Kartika
Sukla 1.

The table (No. 20 on p. 249) shows the scheme of
the different calendars for the year ^aka 1875
(1953-54). The year contains a mala or adhika month.

It may be seen from the above mentioned table
that in case of the light half of the month (sudi half)
the month has the same name for the two systems of
month-reckoningsi but in the dark half of the month
(vadi half) the names of the months in the two systems
are different.

The year-beginnings of the Samvat era in the three
systems of luni -solar calendar are also different, as may
be seen from the following table.

Table 19 — Showing the year-beginnings of the
different systems of Samvat era.

Calendar Caitradi
system

Safnvat era 2010

Agadhadi
system

2010

Kartikadi
system

2010

Beginning

of year Caitra S 1 Asadha S 1 Kartika S 1
(16 Mar., 1953) (12 July, 1953) (7 Nov., 1953)

248

REPORT OF THE CALENDAR REFORM COMMITTEE

Counting of the Succession of Days

In all the calendars used in India, days are counted
according to the solar reckoning, as well as according
to the lunar reckoning {i.e., by tithi or lunar day).
But there is a difference in emphasis.

In the eastern regions (Bengal, Orissa and Assam),
and in Tamil Nad and Malabar, the solar reckoning is
given more prominence. The almanacs give solar
months and count the days serially from 1 to 29, 30,
31 or 32 as the case may be. The tithi endings are
given for every day, and the tithi may start at any
moment of the day.

In other parts of India (except Bengal, Orissa,
Assam and Tamil Nad), the counting of days is based
on the lunar reckoning, and the number of the tithi
current at sunrise is used as the ordinal number of
the date necessary in civil affairs. So there are 29 or
30 days in a month, but the days are not always
counted serially from 1 to 29 or 30.

The month in the lunar calendar is divided into
two half-months, the sudi and vadi halves in the new-
moon ending system, and the vadi and kudi halves in
the full-moon ending system. In fact the year is
divided into 24 half-months instead of 12 months. So
there are 14 to 15 days in a half-month {vide Table 20).

The tithi or lunar day is measured by the positions
of the moon and the sun. When they are in conjunc-
tion, i.e., at new-moon the 30th tithi or amavasya ends
and the first tithi starts which continues upto the
moment when the moon gains on the sun by 12° in
longitude. Similarly when the difference between the
moon and the sun is 24° the second tithi ends, and so
on. The average duration of a tithi is 23 h 37 . m 5, but
the actual duration of a particular tithi undergoes
wide variations from the above average according to
the different positions of the sun, the moon and the
lines of their apsides. It may become as great as
26 h 47 m and as small as 19 b 59 m . So generally to every
day there is a tithi. But sometimes a tithi begins and
ends on the same civil day, and such a tithi is dropped ;
and some religious ceremonies of auspicious character
are not allowed to take place on such a tithi, and the
following day begins with the next following tithi.
For example, if the third tithi is dropped, the sequence
of days of the half-month is 1, 2, 4, 5 etc., thus the
seriality is broken here.

As opposed to the above-mentioned case, the tithi
sometimes extends over two days, there being no tithi
ending in a day (from sunrise to next sunrise). As the
same tithi remains current on two successive sunrises,
the same tithi-numbex is allotted to both the days j
in the second day, however, it is suffixed by the term

'adhiha*. For example if the third tithi is repeated,
then the sequence of days of the half-month would be
1, 2, 3, 3 adhiha, 4, etc.

Some improvement in the use of tithi for dating
purposes is, however, observed in the Fusli calendar
in vogue in some parts of Northern India. In this
calendar the month begins from the day following the
full- moon and dates are counted consecutively
from 1 to 29 or 30 without any break at new-moon, or
any gapping or over-lapping of dates with k$aya tithi
or adhiha tithi. In fact the dates of 'this calendar
have no connection with iithis after the starting of
the month has been determined. The year of Fusli
begins after the full-moon day of lunar Bhadra

Mala Masa and Kshaya Masa

It has been stated before that even at the beginning
of the Siddhanta Jyotisa period, the intercalary months
{mala or adhiha) were determined on the basis of the
mean motions of the sun and the moon, and as such
there was no possibility of the occurrence of any so
called ksaya or decayed month. But as already
mentioned, from about 1100 A.D., the intercalary
months are being determined on the basis of the
true motions of the luminaries, i,e., on the actual
lengths of the new-moon-ending lunar month and
of the different solar months as obtained from
Siddhantic rules. This gave rise to the occurrence
of ksaya months, and the intercalary months
were also placed at very irregular intervals.

The period from new-moon to new-moon (the lunar
month ) is not a period of fixed duration ; it varies
within certain limits according to the different
positions of the apse line of the lunar and solar orbits,
as follows : —

Length of the Lunation

By mean motion According to S.S. Modern

a li d h d h

29 6.3 29 5.9
29 12.73 to to

29 19.1 29 19.6

Comparing these values with the actual lengths of
solar months given in Table 24, it is observed that the
minimum length of the lunar month falls short of all
the solar months, even of the shortest month of Pawa.
But as a mala masa is not possible in that month, the
maximum and minimum limits of the lunar months are
recalculated for each of the solar months from
Kartika to Fhalguna separately.

INDIAN CALENDAR
Table 20.

Scheme of the Lani-Solar Calendar

( Saka 1875 = 1953-54 A.D. )

249

Religious Calendar

Civil Luni-Solar Calendar

Mukkya or new-
moon ending

Caitra S

Caitra K

Vai&akha S
(mala)

Vamkha K
(mala)

Vaisakha S
(suddha)

Vaisakha K
(suddha)

Jyestha S

Jyestha K

Asadha S

Asadha K

Sravana S

Sravana

Bhadra

Asvina

Kartika

Marga.

Marga
Pausa
Pausa
Magha
Magha
Phalguna S
Phalguna K

K
S
K
S
K
S
K
S
K
S
K
S
K

Gauna or full-
moon ending

Caitra S

Vaisakha K

Vai&ahha S
(mala)

Vaisakha K
(mala)

Vaisakha S
(suddha)

Jyestha K

Jyestha
Asadha
Asadha

S
K
S

travail a E
Sravana S
Bhadra
Bhadra
Asvina
Asvina
Kartika
Kartika
Marga.
Marga.
Pausa
Pausa
Magha
Magha
Phalguna K
Phalguna S
Caitra K

K
S
K
S
K
S

Full-moon
ending

Caitra S

Vaisakha V

Vaiixkha S
(adhika)

Vaisakha V
(adhika)

Vaisakha 3
Jyestha V

New-moom
ending

Jyestha
Asadha
Asadha

oravana

Sravana

Bhadra

Asvina

Kartika

Marga.

Pausa

Magha
Magha
Phalguna
Phalguna S
Caitra V

V
S
V

Caitra S
Caitra V
Vamkha S
(adhika)

Vaiiakha V
(adhika)

Vaisakha S
Vaisakha V

Jyestha S
Jyestha V
Asadha S
Asadha
Sravana
Sravana
Bhadra
Bhadra
Asvina
Asvina
Kartika
Kartika
Marga.
Marga.
Pausa
Pausa
Magha
Magha
Phalguna S
Phalguna V

V
S
V

Initial date reckoned on the
Solar Calendar as is now
in use.

Indian Solar
Calendar date

2 Caitra
17 Caitra
1 Vaisakha

17 Vaisakha

31 Vaisakha
15 Jyestha

29 Jyestha
14 Asadha
28 Asadha
11 Sravana
25 Sravana
9 Bhadra
24 Bhadra
8 Asvina
23 Asvina
6 Kartika
21 Kartika

5 Agrah.

21 Agrah.

6 Pausa

22 Pausa
6 Magha

21 Magha

6 Phalguna

22 Phalguna
6 Caitra

Gregorian date

16 Mar.
31 Mar.
14 Apr.

30 Apr.

14 May
29 May

12 June

28 June

12 July

27 July

10 Aug.

25 Aug.
9 Sep.

24 Sep.

9 Oct.

23 Oct.

7 Nov.

21 Nov.

7 Dec.
21 Dec.

6 Jan, 1954
20 Jan.

4 Feb.
18 Feb.

6 Mar.
20 Mar.

S — $ukla paksa or
K = Krsna paksa.

Sudi.

When the lunar month
nearly covers the
Solar month of

Kartika or Phalguna
Agrahayana or Magha
Pausa

V= .

Length of the lunar month.
Minimum Maximum

29 9.7
29 10.5
29 10.8

29 18.0
29 18.8
29 19.1

or Vadi.

Comparing the above limits with the actual lengths
of months stated before, it is found that the minimum
length of the lunar month falls short of all the solar
months except Pausa. So a malamdsa or intercalary
month is possible in all the months except * the month
of ibtisd only.

250

REPORT OF THE CALENDAR REFORM COMMITTEE

The maximum duration of a lunar month, on the
other hand, exceeds the lengths of the solar months
only in case of solar Agrahdyana, Pausa and Magha. So
a ksaya month is possible only in these three months.

A list is given below showing the actual intercalary
months occurring during the period Saka 1823 (1901-2
A. D. ) to Saka 1918 (1996-97 A. D. ) on the basis of
Surya Siddhanta calculations.

Table 21.

Intercalary months in the present century

tvaka

Saka

1823

bravana

1872

Asadha

1826

Jyaistha

1875

Vaisakha

1828

Caitra

1877

Bhadra

1831

Sravana

1880

Sravana

1834

Asadha

1883

Jyaistha

1837

Vaisakha

1885*

Asvina, Caitra

1839

Bhadra

1888

Sravana

1842

Sravana

1891

Asadha

1845

Jyaistha

1894

Vaisakha

1847

Caitra

1896

Bhadra

1850

Sravana

1899

Asadha

1853

Asadha

1902

Jyaistha

1856

Vaisakha

l904**Asvina-Phal.

1858

Bhadra

1907

Sravana

1861

Sravana

1910

Jyaistha

1864

Jyaistha

1913

Vaisakha

1866

Caitra

1915

Bhadra

1969

Sravana

1918

Asadha

Pausa is Ksaya,

* + Magha is Ksaya.

As regards the ksaya months that occurred and
will be occurring during the period from 421 Saka
(49S-500 A D.) to 1885 iSaka (1963"64 A.D.) a statement
is given below showing all such years mentioning the
month which is ksaya and also the months which are
adhika in these years. The calculations are based on
Surya Siddhanta without bija corrections upto 1500
A. D. arid with these corrections after that year.

Table 22 — K§aya or decayed months

&aka

A.D.

Ksaya month

Adhika months before

and after the Ksaya

month

448

526-27

Pausa

Kartika, Phalguna

467

545-46

Pausa

Kartika, Phalguna

486

564-65

Pausa

Asvina, Phalguna

532

610-11

Margasirsa

Kartika, Vaisakha

551

629-30

Pausa

Asvina, Caitra

692

770-71

Pausa

Asvina, Caitra

814

892-93

Margasirsa

Kartika, Caitra

838

911-12

Pausa

Asvina, Caitra

974

1052-53

Pausa

Asvina, Caitra.

Saka

A.D.

Ksaya month

Adhika month

1115

1193-94

Pausa

Asvina, Caitra

1180

1258-59

Pausa

Kartika, Caitra

1199

1277-78

Pausa

Kartika, Phalguna

1218

1296-97

Pausa

Marga., Phalguna

1237

1315-16

Margasirsa

Kartika, PhlUguna

1256

1334-35

L ausa

Asvina, Phalguna

1302

1380-81

Margasirsa

Kartika, Vaisakha

1321

1399-1400

Pausa

Kartika, Caitra

1397

1475-76

Magha

Asvina, Phalguna

1443

1521-22

Margasirsa

Kartika, Vaisakha

1462

1540-41

Pausa

Asvina, Caitra

1603

1681-82

Pausa

Asvina, Caitra

1744

1822-23

Pauga

Asvina, Caitra

1885

1963-64

Pausa

Asvina, Caitra

It will be observed from the above table that
according to Surya Siddhanta calculations one ksaya
month occurs on average after 63 years. But one
may repeat as soon as after 19 years and as late as
after 141 years. In rare cases they recur after 46, 65>
76 and 122 years.

Intercalary months according to
modern calculations

The lunar calendar proposed by the Committee for
religious purposes is based on the most up-to-date
value of the tropical year and the correct timings of
new-moon. As such the intercalary months according
to these calculations would not always be the same
as determined from Surya Siddhanta-Cd\cu\aX.ions and
shown above, The intercalary {mala or adhika) and
decayed {ksaya) months according to these calculations
are shown below for Saka years 1877 to 1902.

Table 23 — Intercalary month according
to modern calculations.

Saka A.D

Saka

1877
1880
1883
1885

1888
1891
1894

A.D

1955-56
1958-59
1961-62
1963-64

1966-67
1969-70
1972-73

Intercalary
Month

1896
1899
1902

Bhadra

Sravana

Jyaistha

Kartika & Caitra
(A.grahayana ksaya

Sravana
Asadha
Vaisakha

1974-75
1977-78
1980-81

Intercalary
Month

Bhadra

Sravana

Jyaistha

Proposal of the Committee about the Lunar Calendar

According to the Siddhantic rules, the lunar
calendar is pegged on to the solar calendar, and so
it is the luni-solar calendar with which we are at
present concerned. It has already been shown that
the length of the Surya Siddhanta year is greater than
the year of the seasons {i.e., the tropical year) by
about 24 minutes. As a result of this the seasons have

INDIAN CALENDAR

251

fallen back by about 23 days in our solar calendar.
The lunar calendar, being pegged on to the Siddhantic
solar calendar, has also gone out of seasons by about
the same period, and consequently religious festivals
are not being observed in the seasons originally
intended.

The solar (saura) month for the religious calendar

Although the Committee considers that the solar
year to which the religious lunar calendar is to be
pegged on should also start from the V. E. day, it felt
that the change would be too violent ; with a view
to avoiding any such great changes in the present day
religious observances, it has been considered expedient
not to introduce for sometime to come any discon-
tinuity in this system, but only to stop further -increase
of the present error. The solar year for the religious
calendar with Vaisakha as its first taura month should
now commence when the tropical longitude of the sun
amounts to 23° 15\ This saura month will determine
the corresponding lunar months required for fixing the
dates of religious festivals. The lengths of such
months, which are also fractional, are stated below,
giving the lengths according to the Surya Siddhanta
calculations compared with the corresponding modern
values.

Table 24— Lengths of Solar months
of the Religious Calendar.

Lengths of Months

Saura

Long, of

Accorditig to Surya

Modem

Mdsa

Sun

Siddhanta

Value

(1950 A.D.)

Vaisakha

23°

15'—

30 d 22 h

30 d 20 h 55 m

Jyaistha

15—

6 39

Afladha

15—

10 53

Sravana

113

15—

8 22

Bhadrapada

143

15—

23 51

Asvina

173

15—

11 51

Kartika

203

15—

23 41

Margasirsa

233

15—

14 33

Pausa

263

15—

10 40

Magna

293

15—

12 57

Phalguna

323

IS-

20 54

Caitra

353

IS—

8 33

365

5 49

The. lengths of the months according to the Surya
Siddhanta are the same as shown . earlier, as the
same month was used by the S. S. for both the
purposes. But the modern value, is different from
that shown before, due to the fact that a different
point is taken here for the beginning of months.
The modern value is, however, not fixed for all
times, but it undergoes slight variation as explained
previously.

The luni-solar calendar by which the religious
festivals are determined has been pegged on to the
religious solar calendar starting from a point 23° 15'
ahead of the V. E. point. As this religious solar
calendar is based on the tropical year, the luni-solar
calendar pegged on to it would not go out of the
seasons to which they at present conform, and so the
religious festivals would continue to be observed in the
present seasons and there would be no further shifting.

The Committee has proposed that the luni-solar
calendar should no longer be used for civil purposes
in any part of India. In its place the unified solar
calendar proposed by the Committee should be used
uniformly in all parts of India irrespective of whether
the luni-solar or solar calendar is in vogue in any
particular part of the country.

5.8 INDIAN ERAS

Whenever we wish to define a date precisely we
have to mention the year, generally current of an era,
besides the month and the particular day of the month,
and the week-day. This, enables an astronomer, well-
versed in technical chronology, to place the event
correctly on the time-scale. In international practice
the Christian era is used, which is supposed to have
started from the birth -year of Jesus' Christ. But as
mentioned in Chapter II, it is an extrapolated era which
came in use five hundred years after the birth of the
Founder of Christianity, and its day of starting may be
widely different from the actual birthday of Christ,
about which there exists no precise knowledge.

In India, nearly 30 different eras were or are used
which can be classified as follows : —

(1) Eras of foreign origin, e.g., the Christian era,
the Hejira era, and the Tarikh Ilahi of Akber.

(2) Eras of purely Indian origin, list given.

(3) Hybrid eras which came into existence in the
wake of Akber's introduction of Tarikh Ilahi.

Table 27 shows purely Indian eras, with their
starting years in terms of the Christian era, the elapsed
year of the era*, the year-beginning, solar, lunar or
both solar and the lunar as the case may be, the parti-
cular regions of India where it is current. Inspite of
the apparent diversity in the ages of the eras, the
methods of calendarical calculations associated with
each era are almost identical ; to be more accurate
only slightly different and follow the rules given in
either cf the three Siddhantas, Surya, Arya and
Brahma. The three methods differ but slightly.

* Generally, but not always the Indian eras have "elapsed
years". Thus year 1876 of 6aka era would be, if we followed
the western convention, year 1877 6aka (current).

C. E. — 40

252

EEPORT OF THE CALENDAR REFORM COMMITEE

The apparent antiquity of certain eras, e.g., the
Kaliyuga or the Saptar& are however rather deceptive,
for these eras are not mentioned either in the Vedic
literature or even in the Mahabharata ( a work of the
4th to 2nd century B.C. ). The best proof, however,
that no eras were used in date-recording in ancient
India is obtained from "Inscriptions" which give 'con-
temporary evidence' of the method of date-recording
in use at the time when the inscription was composed.

In India, the oldest inscriptions so far discovered
and deciphered satisfactorily are those of the Emperor
Asoka (273 to 227 B.C.) ; for the earlier Indus valley
seal recordings have not yet been deciphered and no
inscriptions or seals which can be referred to the time-
period between 2500 B.C. (time of Indus valley civili-
zation) and 250 B.C. ( time of Asoka ) have yet been
brought to light. Asoka mentions in his inscriptions
only the number of years elapsed since his coronation.
No month, week-day or the serial number of the day
in the month is mentioned. A typical Asokan ins-
cription giving time references is given in § 5. 5.

Continuous erak first began to be used in the re-
cords of the Indo-Scythian kings who reigned in
modern Afghanistan and North-Western India bet-
ween 100 B.C. to 100 A.D.

What is then the origin of the Kaliyuga or Saptam
era given in Table 27 which go back to thousands of
years before Christ ? We are going to show presently -
that they are extrapolated eras invented much later
than the alleged starting year.

It is clear from historical records that date-recor-
ding by an era in India started from the time of the
Kusana emperors and Saka satraps of Ujjain. But
India cannot be singled out in this respect, for none
of the great nations of antiquity, viz., Egypt, Babylon,
Assyria or later Greece and Rome, used a continuously
running era till rather late in their history. The
introduction of the era is connected with the develop-
ment of the sense of 'History* which came rather late
to all civilized nations.

Critical Examination of Indian Eras

Here we are examining critically the claims of a
few eras, which are supposed to date much earlier, e.g.,
the Kaliyuga era which is commonly believed to have
heen introduced in 3102 B.C., the Saptar$i era, and
the Pa^ava-Kala mentioned by KalWa, the historian
of Kashmir, who wrote in 1150 A.D., and supposed to
be dating from 2449 B.C., and others.

The Saptarsi era commoly known as Lokakala or
Laukika Kala is measured by centuries and has 27 such

centuries in the total period of the cycle. Each cen-
tury is named after a nak§atrai viz., Asvinl, Bharayi,
etc ; and the'number of years within the century is
generally mentioned, so that the number of year of the
era never exceeds 100. This era was in use in
Kashmir and neighbouring places. In fact this era has
no relation with the seven gsis (the Great Bear) in the
sky or with any actual nak?atra division. There is
difference of opinion as to the beginning of the era.
According to Vrddha Garga and the Puranas the
starting year of the tenth century named after Magha
are 3177 B.C., 477 B.C. and 2224 A.D. of the different
cycles, when according to Varahamihira the third
century named Krttika begins. The beginning
years of Varahamihira s Magha century of the
different cycles are however 2477 B. C, 224 A. D.
and 2924 A.D.

The Pancjava Kala or the Yudhisthira era started
from 2449 B.C. according to Varahamihira.

The so-called Yudhisthira era (2449 B.C.) is given
by Kalhana, chronicler of Kashmir (1150 A.D.), who
quotes the date from Vrddha Garga, an astronomer
whose time is unknown. This era also does not occur
in any inscription or any ancient treatise prior to
Kalhana (1150 A.D.). Prof. M. N. Saha has shown that
in the Mahabharata the Krttikas are in many places
taken as the first of the naksatras and are very nearly
coincident with the vernal equinox. If we calculate
the date of the M.Bh. incidents on this basis, the date
comes out to be very nearly 2449 B.C.

It, however, niether proves that the incidents
mentioned in the M.Bh., if they were actual
occurrences, took place in 2449 B.C., for the epic was
not certainly put to writing before 400 B.C. as we
know from a verse already mentioned on p. 226. It is
inconceiveable to think that the dates could be
remembered correctly for over 2000 years, when
writing was in a very primitive state. The astro-
nomical references in the battle scenes, from which
certain writers very laboriously deduce the date of
these occurrences, are most probably later interpola-
tions, on the supposition that the incidents occurred
about 2449 B.C. There is no inscriptional record
regarding the use of Yudhisthira era or Pan(}avakala.

(a) The Kaliyuga Era

It is easy to show that the Kaliyuga era which
purports to date from 3102 B.C. is really an extra-
polated era just like the Christian era, introduced
long long after the supposed year of its beginning.

It is first mentioned by Xryabha{a, the great
astronomer of ancient Pataliputra, who says that 3600

INDIAN CALENDAR

253

years of the Kaliyuga had passed when he was 23
years old which is Saka year 421 (499 A. D.). It is not
mentioned earlier either in books or in inscriptions.
The first mention of this era in an inscription is found
in the year 634-35 A.D., the inscription being that
of king Pulakesln II of the Calukya dynasty of
BadSml, or somewhat earlier in a Jain treatise. It
was most probably an era invented on astrological
grounds just like the era of Nabonassar, by Sryabhata
or some other astronomer, who felt that the great
antiquity of Indian civilization could not be described
by the eras then in use (Saka, Chedi or Gupta era),
as they were too recent.

What were these astrological grounds ?

The astrological grounds were that at the beginning
of the Kaliyuga, the sun, the moon and the planets
were in one zodiacal sign near the fixed Siddhantic
Mesadi which according to some authorities is
( Piscium % but according to others is 180° from Citra
or a Virginis. This was probably a back calculation
based on the then prevailing knowledge of planetary
motion, but has now been found to be totally wrong,
when recalculated with the aid of more accurate
modern data on planetary motion. We quote from
Ancient Indian Chronology, pp. 35 39 by Prof. P. C.
Sengupta, who has given a full exposition of Burgess's
views on this point, with recalculations of his own.

should also bo a total eclipse of the Sun ; but no such
things happened at that time. The beginning of the
Kaliyuga was the midnight at UjjayinI terminating the
17th February of 3102 B.C., according to Surya Siddhanta
and the ardltanttrika system of Aryabhata's astronomy as
described in the Khatjdaklmdyaka of Brahmagupta. Again
this Kaliyuga is said to have begun, according to the
A.ryabha\iya from the sunrise at Lanka (supposed to be on
the equator and on the same meridian with Ujjain) — from
the mean sunrise on the 18th Feb., 3102 B.C.

Now astronomical events of the type described above
and more specially the conjunction of the sun and the moon
cannot happen both at midnight and at the next mean
sunrise. This shows that this Kaliyuga had an unreal
beginning.

The researches of Bailey, Bent ley and Burgess have
shown that a conjunction of all the 'planets' did not happen
at the beginning of this Kaliyuga. Burgess rightly
observes : 'It seems hardly to admit of a doubt that tlie
epoch (the beginning of the astronomical Kaliyuga) was
arrived at by astronomical calculation carried backward.

We also can corroborate the findings of above research-
ers in the following way and by using the most up-to-date
equations for the planetary mean elements.

Now the precession of the equinoxes from 3102 B. C.
to 499 A. D. or Aryabhata's time works out to have been
= 49° 32' 39". The mean planetary elements at the beginning
of the Kaliyuga, i.e., 17th Feb., 3102 B.C., UjjayinI mean
time 24 hours, are worked out and shown below. We have

Table 25 — Longitudes of Planets at Kali-beginning.

Mean Tropical
longitudes on
Planet Feb. 17, U.M.T.

24 hrs., 3102 B.C.
(Moderns.)

Sun
Moon
Moons Apogee
Moon's Node
Mercury
Venus
Mars
Jupiter
Saturn

Longitude at the same
time measured from the
Vernal Equinox of 499
A.D,, i.e., Aryabhata's
time.

The same as assumed in
the Ardhardtrika system
at the same time as j
before and also at next j
mean sunrise. j

Error in the assumption
of Aryabhata and also of
the modern Surya-
Siddhanta and the
KUanda k h ad ya ka .

301°

40'

9.22"

351°

12'

48"

0°

+ 8°

47'

12"

305

13.81

355

+ 4

27.66

- 3

147

15.05

196

180

-16

268

1.65

317

+ 42

334

50.25

-24

290

54.67

339

+ 20

318

45.74

- 8

282

15.07

I 331

+ 28

" Astronomical Kaliyuga an Astronomical Fiction 9 '

At the beginning of the astronomical Kaliyuga, all the
mean places of the planets, viz., the Sun, Moon, Mercury,
Venus, Mars, Jupiter and Saturn, are taken to have been in
conjunction at the beginning - of the Hindu sphere, the
moon's apogee and her ascending node at respectively a
quarter circle and a half circle ahead of the same intial
point. Under such a conjunction of all the planets, there

added 49° 32' 39" to these mean tropical longitudes arrived
at from the rules used, so aw to got tho longitudes measured
from the vernal equinox of Aryabhata's time.

Hence we see that tho assumed positions of the moan
planets at the beginning of the astronomical Kaliyuga tvoro
really incorrect and the assumption was not a reality. But
of what use this assumption was in Aryabhata's time, i.e.,
499 A.D., is now set forth below.

254

REPORT OF THE CALENDAR REFORM COMMITTEE

Aryabha^a says that when he was 23 years old, 3600
years of Kali had elapsed. According to his Ardharatrika
system :

3600 years=»'l/l200 of a Mahayuga = 1314931.5 days.
Again according to his Audayika system :

3600 years =1/1200 of a Mahayuga^ 1314931.25 days.

Hence according to both these systems of astronomy of
Aryabhata, by counting 3600 years from the beginning of
the astronomical Kali epoch, we arrive at the date March
21, 499 A.D., tjjjayini mean time, 12 noon. The unreality
of the Kali epoch is also evident from this finding.
However, the position of mean planets at this time work
out an given in table 26 below.

about 57 B. C. Moreover a critical examination of
inscriptions show the following details about this era.

The earliest mention of this era, where it is
definitely connected with the name of king Vikramtf-
ditya is found in an inscription of one king Jaikadeva
who ruled near Okhamandal in the Kathiawar State.
The year mentioned is 794 of Vikrama era, i.e., 737
A.D. In a subsequent inscription, dated 795 V.E. it
is also called the era of the lords of Mslava. So the
Vikrama era and the era of Malava lords are one and
the. same. Tracing back, we find the Malavagana era
in use by a family of kings reigning at Mandasor,
Rajputana between the years 461-589 V.E., as feuda-

Table 26 — Longitudes of Planets at 3600 Kaliyuga era.
Date : March 21, 499 A.D Ujjayini Mean Midday.

Mean Long.

Mean Long.
Moderns.

. Error in the

Planet

Ardharatrika

Audayika

system.

Sun

0° 0'

359°

42' 5"

+17' 55"

Moon

280 48

280

24 5a

+23 8

Moon's Apogee

35 42

24 38

+17 22

Moon's Node

352 12

352

2 26

+ 9 34

Mercury

180

186

183

9 51

+2° 50' 9"

Venus

356 24

356

7 51

+16 9

Mars

7 12

52 45

+ 19 15

Jupiter

186

187 12

187

10 47

+ 1 13

Saturn

49 12

21 13

+50 47

It is thus clear that the beginning of the Hindu
astronomical Kaliyuga was the result of a hack calculation
wrong in its data, and was thus started wrongly.

It is also established that the astronomical Kaliyuga-
reckoning is a pure astronomical fiction created for facilita-
ting the Hindu astronomical calculations and was designed
to be correct only for 499 A.D. This Kali-reckoning
cannot be earlier than the date when the Hindu scientific
Siddhantas really came into being. As this conclusion
<jannot but be true, no Sanskrit work or epigraphio
evidences would be forthcoming as to the use of this
astronomical Kali-reckoning prior to the date 499 A.D".

(b) The Vikrama Era

The Vikrama Era is widely prevalent in Northern
India? excepting Bengal, and used in inscriptions from
the ninth century A.D. Let us probe into its origin.

In popular belief, the Vikrama era was started
by king Vikramaditya of Ujjain who is claimed to
have repelled an attack on this famous city by Saka
or Scythian hordes about 57 B. C. and founded an
era to commemorate his great victory.

Unfortunately no historical documents or inscrip-
tions have yet been discovered showing clearly the
existence of a king Vikramaditya reigning at Ujjain

tories to the Imperial Guptas ( 319-§50 A.D. ). They
call it not only the era of the Malava tribe* but also
alternatively as the Krta era. A number of inscrip-
tions bearing dates in the Krta era have been found in
Rajasthan, and the earliest of them goes back to the
year 282 of the Krta era (The Nandsa Yupa inscription
described by Prof. Altekar, Epigraphia Indica, Vol.
XXVII, p. 225).

From these evidences, it has been concluded by
historians that the earliest name so far found of this
era was Krta. What this means is not clear. Then
between 405-542 A.D., it came to be known as the
era of the Malava tribe and was used by the Verma
kings of Mandasor, Rajputana, though they were
feudatories of the Gupta emperors (319-550 A .p.). Its
association with king Vikrama is first found in the
year 737 A.D., nearly 800 years after the supposed
date of king Vikrama. Its use appears to have been
at first confined to Kathiawar and Rajasthan, for the
whole of Northern India used between 320 A.D. to
600 A.D., the Gupta era, which fell into disuse with
the disappearance of the Gupta rule in 550 A.D. For
a time. Northern India used the Harsa era introdu-
ced by the emperor Harsa Vardhana (606 AJD.), but
when the Gurjara-Pratihars, who came from

INDIAN CALENDAR

255

JUjasthan, conquered the city of Kanauj about 824
A.D., they brought the Vikrama era from their original
home, and it became the current era all over northern
Inciia except the eastern region, and was used by all
Rajput dynasties of medieval times.

The months of the Vikrama era are all lunar, and
the first month is Caitm. The months begin after the
full-moon but the year begins 15 days after the full-
moon of Phalguna, i.e. after the new-moon of Caitra*
But for astronomical calculations, it is pegged on to a
solar year, which starts on the first of solar Vaisakha,
theoretically the day after the vernal equinox. The
Vikrama era is current also in parts of Gujrat, but
there the year begins in KSrttka and the months are
amanta, which corresponds to the Macedonian month
of Dios, and the epoch is just six months later.
Thus the western and northern varieties of the
Vikrama era follow respectively the Macedonian and
Babylonian reckonings (see § 3.3), the year of starting
is 255 years later than that of the Seleucidean era.

The conclusion is that the champions of the
Vikrama era have still to prove the existence of king
Vikrama of Ujjain. Early inscriptions show that the
method of date-recording is not typically Indian as in
the Satavahana inscriptions but follow the Saka-KusSna
method, which fpllows the contemporary Graeco-
Chaldean method. It was therefore a foreign recko-
ning introduced either by the Greeks or Sakas, or
an Indian prince or tribe who had imbibed some
Graeco-Chaldean culture, but was adopted by the
Malava tribes who migrated from the Punjab to Rajas-
than about the first century B.C. The association
with a king Vikrama occured 800 years later, and is
probably due to lapse of historical memory, for the
only historical king VikramSditya who is known to
have crushed the Saka power in Ujjain, was king
Candragupta II of the / Gupta dynasty (about 395
A.D.). Before this, the Saka dynasty in Ujjain had
reigned almost in unbroken sequence from about 100
A.D. to 395 A.D., and ^had used an era of their
own, later known as the 'Saka' era. All the Gupta
emperors from Samudragupta, had an "Aditya" title,
and many of them had the title "Vikramaditya" so
that the Gupta age was par excellence the age of
Vikramadityas. But all the Gupta emperors use in
their inscriptions the family era called the Guptakala
which commemorated the foundation of Gupta empire
(319 A.D.). The association of the Malava era with king
VikramSditya, and assignment of king VikramSditya
to Ujjain, was due to confusion of historical memory
not infrequent in Indian history. It may be' mentioned
that the Vikrama era is never used by Indian astro-
nomers for their calendaric calculations, for which
puapose the Saka era is exclusively used.

Hie Saka Era is the era par excellence which has
been used by Indian astronomers all over India in their
calculations since the time of the astronomer Varaha-
mihira (died 587 A.D.) and probably earlier. The
Indian almanac-makers, even now, use the Saka era
for calculations, and then convert the calculations to
their own systems.

This era is extensively used over the whole of India
except in Tinnevelly and part of Malabar, and is more
widely used than any other era. It is also called Saka
Kala, Saka Bhtlpa Kala, Sakendra Kala, and Salivahana
Saka and also Saka Samvat. Its years are Caitradi for
luni-solar reckoning and Me$adi for solar reckoning.
In the luni-solar reckoning the months are purnirnanta
in the North and amanta in Southern India. The
reckoning of the Saka era begins with the vernal equi-
nox of 78 A.D., and is measured by expired years, so
the year between the vernal equinox of 78 A.D. to that
of 79 A.D. is zero of Saka era. In some pancangas or
Southern India the current year is however seen to be
used instead of the elapsed year, where the number of
year of the era is one more than the era in general use
But we are not yet sure about the origin of this
era. It has been traced back to the Saka satraps of
Ujjain, from the year 52 (130 A.D.) to the end of the
dynasty about 395 A.D. But in their own records,
they merely record it as year so and so, but there is
not the slightest doubt that the era used by them
subsequently became known as the Saka era (vide § 5.5).
The Old and the New Saka era.
The dates given by different authorities about the
starting year of the old Saka era mentioned in § 5.5
vary from 155 B.C. to 88 B.C. as given below :
Konow ; 88 B.C. (date of death of Mithradates II, the
powerful Parthian emperor who is
said to have subjugated the Sakas).
Konow has proposed a number of other dates.
Jayaswal : 120 B.C. :

Herzfeld : 110 B.C. : Settlement of the Sakas in

Seistan by Mithradates II.
Rapson : 150 B.C. : Establishment of the 8aka

kingdom of Seistan.
Tarn : 155 B.C. : Date of settlement of the Saka

immigrants in Seistan by
Mithradates I.
Recently Dr. Van Lohuizen de Leeuw has discus-
sed the starting point of this era in her thought-provok-
ing book 'The Scythian Period of Indian History*. She has
rejected all the above dates, and fixed up 129 B.C. as
the starting date of the old Saka era. She identifies this
year as the one in which the Sakas, descending from
the Trans-Oxus region, attacked the Parthian empire

256

in which the Parthian emperor Phraates II was defea-
ted and killed, and the rich province of Bactna was
occupied by the Sakas. They founded an era to com-
memorate their victory over the Parthians which their
successors took to India, as they expanded and put an
end to the Bactrian Greek principalities in Afghanistan
and north-west Punjab. She suggests that the old
Saka era was also used by the Kusanas, who were
after all a Sakish ruling tribe, but from the time of
Kaniska with hundreds omitted.

Dr. M. N. Saha has supported this theory in its
main features, but he thinks that the era was founded
in 123 B C , for he shows from historical records that
I the Sakas assailed Bactria first in 129 B.C. and entered
! into a seven year conflict with the Parthians, and
! finally conquered Bactria in 123 B.C., when the Par-
thian emperor Artabanus II, was defeated and killed.
Probably the Sakas then founded their era. This Was
also called the era of Azes. Dr. Van Lohuizen de
Leeuw has accepted Sana's suggestion.

This hypothesis, though not finally settled appears
to- have , a good deal of probability, for the following
reasons :

Dr. Saha points to the fact that Indian classics,
which can be dated from the third century B.C. to the
second century A.D., mentions three races in what is
modern Afghanistan and N. W. India, viz., the Sakas,
the Yavanas, and the Pallavas, who attained to the
status of ruling races. The order in which they are
mentioned denotes correct chronological sequence, for
they are arranged in the order of their chronological
appearance in history, the gakas being mentioned as a
subject race in Darius's inscription (518 B.C.). But
the Yavanas (Greeks) were the first to attain the status
of a ruling race, from 312 B.C., the date of foundation
of the Seleucid empire, whose power in the west was
overthrown by the Parthians, or Pehlevis (Pallavas of
Indian classics) in 248 B.C.

Both these ruling races of Yavanas and Pallavas
used eras of their own, viz., the Seleucidean era from
312 B.C., and the Parthian era from 248 B.C. Did the
third race, the Sakas who were the last to attain
status of a ruling race ever use an era of their own ? It
would be surprising if they did not, for it became the
fashion for all races, who attained the status of ruling
people, to have eras of their own. The early Sakas,
as their records show, were deeply influenced by their
neighbours to the west, viz., the Parthians who adopted
Greek culture, and their coin-records show that they
also adopted Greek culture, and therefore most
prbbably. the Graeco-Chaldeah method of date
recording.

REPORT OF THE CALENDAR REFORM COMMITTEE

The points given in § 5.5 and above may be
summarized as follows : —

(a) The Sakas starting from Central Asia attacked
the Parthian empire in 129 B.C., and overcame
Parthian resistance by 123 B.C. It is very probable
that they started an era to commemorate their
accession to power in Bactria from 123 B.C. They used
Macedonian months and Graeco-Chaldean methods of
calendaric calculations as prevalent in the Seleucid
and Parthian dominions. Probably the era was some-
times named after Azes, who was probably their leader.
But this Azes is not to be confounded with later
Azes I or Azes II, who reigned in Taxila between 40
B.C. and 20 B.C. Within the first 200 years of its
starting/the era was alternatively called the Azes era.

(b) This Saka era ( known to archaeologists as the
old Saka era ) was used by the Saka emperors and Saka
satraps in their Indian territories, but the time-
reckoning began to ba gradually influenced by Indian
customs. They began to use Indian months alter-
natively with Macedonian months and Pur'nimanta
months in place of Am&nta months. During the first
200 years, the hundreds were sometimes omitted, in
the use of the era.

(d) The Saka era was used by the house of Castana
of Ujjain with 200 omitted, but gradually they forgot
the origin of the era and continued their own reckoning
without further omission of hundreds upto the end of
the Saka satrapal rule over UjjainI about 395 A.D. As
the early Indian astronomers were mostly of foreign
origin (viz. Sakadvlpi Brahmana) the astronomical
reckonings necessary for compiling the calendar were
carried out using the Saka era and Graeco-Chaldean
astronomy. The blending of Graeco-Chaldean
astronomy as known about the early years of the
Christian era with older Indian calendarica^ features
formed the basis of Siddhanta Jyotisa. The Sakadvlpi
Brahmins also brought to India horoscopic astrology
using the Saka era exclusively in horoscopes, a custom
which has persisted to this day. These facts explain
the pre-eminence of the Saka era.

(d) Other Eras

Buddha Nirvana Era .—The Buddhists of Ceylon
have been using since the first century B.C. the
Buddhist Nirvana* era, having its era-beginning in 544
B.C. This era has not however been found in use on
the Indian soil, except for a solitary instance in
an inscription of Asokachalla Dev found at Gaya
dated in the year 1813 of the Buddhist Nirvana

INDIAN CALENDAB

257

era — 1270 A.D. Most of the antiquarians however
put the date of Nirvana in 483 B.C. The origin of
the Buddha Nirvana era used in Ceylon has not yet
been satisfactory explained.

The Gupta Era : — This era was clearly ] established
by the founder of the Gupta dynasty (Candragupta I)
to commemorate the accession to imperial power of
his family, about 319 A.D., and was in vogue over the
whole of Northern India from Saurashtra to Bengal
during the days of their hegemony (319 A.D.-550 A.D.).
After the decay of their empire, the era was continued
by their former vassals, the Maitrakas of Vallabhi and
was in use in parts of Guzrat and Rajputana up to
the thirteenth century. Its use in Bengal was discon-
tinued from about 510 A.D. with the disappearance
of Gupta rule first in South Bengal, then over the
whole of Eastern India. In the Uttar Pradesh (ancient
Madhyadesa), it was driven out by the Harsa era,
which had a short period of existence, 606-824 A.D.,
when the city of Kanauj was occupied by king
Nagabhata of the PratihSr dynasty, who hailed from
Rajasthan. The Pratihars brought with them the
Vikrama era, . which had been current in Rajasthan,
and this became the great era of the north, used by
all medieval Rajput dynasties, except those belonging
to the eastern region.

Eras in Eastern India

Most parts of Bengal were under the Gupta
emperors, and used the Gupta era during their
hegemony (319-510 A.D.). But Gupta rule disappeared
as mentioned above from major parts of Bengal from
<ra. 510 A.D., and the subsequent dynasties including
the Pala emperors ( 750 A.D —1150 A.D. ) used regnal
years in their inscriptions for four hundred years of
their rule. The Saka era in Bengal appear to have been
introduced by the Sena dynasty which replaced the
Palas ; the Senas were migrants from the south
{ Karnata-Ksatriyas ), where they were familiar with
the Saka era, but it was not used in royal records
which continued to use regnal years. The Vikrama
Samvat never became popular in Bengal, or Eastern
India. After Mohamedan conquest, Bengal was left
without an era. For official purposes, Hejira was
used, But the learned men used the Saka era, and the
common people in certain parts used a rough reckoning,

called Parganati'AMa, reckoned from the time of
disappearance of Hindu rule.

After the introduction of Tarikh Ilahi, the people
of Bengal began to use the Sarya Siddhanta reckoning,
and the solar year. The Bengali San had thus a
hybrid origin ; to find' the current year of the Bengali
San, we take Hejira year elasped in 1556, i.e., 963 and
add to it the number of solar years. Thus 1954
A. D. is 963 A.D. + (1954 -1556) -1361 of Bengali San,

Other hybri eras

A number of other hybrid eras formed in a similar
way to Bengali San is mentioned in the table (No. 27) :
Amli and Vilayati in Bengal and Orissa, the various
Fasli or harvest years in Bengal, Deccan, and
Bombay.

All the other eras mentioned as hybrid in the
chart were formed in a similar way, and the slight
differences are due to mistakes in calculation, or
differences in the time of introduction. While the
Bengali San has Mesadi as year-beginning, others
have taken the year-beginning to be coincident with
some important mythical event of local provenance,
e.g., the year-beginning of the Amli era used in
Orissa, viz., the 12th lunar day of the light half of the
month of Bhadra is said to represent the birth date
of king Indradyumna, the mythical king who is said
to have discovered the site of modern Puri. The
great temple of Puri was actually built by king
Anyanka Bhim Dev of the Ganga dynasty about 1119
A.D., and kings of this dynasty who held sway in
Orissa from 1035-1400 A. D, used the Ganga era,

The Kollam era prevalent in the Malayalam
countries is of obscure origin. The year of this era
is known as the Kollam Anclu. The era is also called
the Era of Parasurama, and is said to have omitted
thousands from their previous reckonings. In South
Malabar it begins with the solar month Simha and
in North Malabar with the solar month Kanya.
The era started from 825 A.D.

The Jovian cycle : In Southern India the years are
named after the name of the Jovian year and so it also
serves the purpose of an era of a short period, viz., 60
years, after which the years recur. Details about
Jovian years will be found in Appendix 5-E.

[ 258

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APPENDIX 5-A

The Seasons

We have seasons because the celestial equator is oblique
to the sun's path (or the ecliptic), or in modern parlance,
the axis of rotation of the earth is not perpendicular to its
orbit, but inclined at an angle of 66*°. This causes varying
amounts of sunlight to fall on a particular locality through-
out the year. If the earth's axis were perpendicular to the
ecliptic, in other words the obliquity were zero, every
portion of the earth from the equator to the pole would
have had 12 hours of sunlight, and 12 hours of shade.
There would have been no seasons on any part of the earth,
just as we have now for places on the earth's equator, where
we have no variation of season throughout the year, because
the day and night are equal for all days of the year.

It can be proved from spherical trigonometry that the
duration of sunlight for a place having the latitude <t> is
given by

12+tV Sin" 1 ( tan <p tan S ) hours,
where 8= declination of the sun on that day ; 8 being
counted positive when it is north of the equator, and
negative when south.

If S is negative, i.e., when the sun is south of the
equator, the second term of the above equation is negative,
and daylight will be of less than 12 hours' duration.

This holds up to the latitude of ^— € = 66*°, i.e., the

beginning of the arctic zone. Between the arctic circle
and the north pole, the sun will remain constantly above
the horizon more than twenty-four hours for several days
together during the year. Thus at a place on 70° north
latitude, the continuous day is observed for 64 days from
21st May to 24th July, at 80° north latitude it is for 133
days from 17th April to 28th August, at the north pole it
is for six months from 21st March to 23rd September. -

For a person on the north pole, the sun will appear on.
the horizon on the vernal equinox day, and will go on
circling round the sky parallel to the horizon and rising
every day a little up, till on the solstitial day, he attains
the maximum altitude, viz., 23° 27'. After that the sun
will begin to move down and on the day of autumnal
equinox, will pass below the horizon. Thus for six
months, from 21st March '(V.E.) there will be continuous
day for a person on the north pole, and from the 23rd Sept,
(A.B.) to the. next 21st March (V.E.), there will be a
continuous night for six months.

The position described above is for the northern hemis-
phere, viz.j for those dwelling north of the equator. In the
southern hemisphere the position is just reversed ; when
the day is longer in the northern hemisphere, it is shorter
in the southern hemisphere.

The amount of daylight received at any place determines
the season. When we have maximum sunlight, we have
the hot season. When we have minimum sunlight, we shall
have winter. The other seasons come in-between. Bain,
frost, etc., are secondary effects produced by varying
amounts of sunlight, and of the atmospheric conditions
stimulated by the sunlight received. The sun is the sole
arbiter of the seasons.

Hence the definitions of seasons as given by the ancient
astronomers, whether Western and Indian, which base them
on the cardinal days of the year, are the only correct
definitions. A system which deviates from this practice is
wrong.

The majority of the Indian calendar makers have not,
however, followed this definition. The reason is more
psychological than scientific. For along with astronomy,
there has been also a growth of astrology which has fixed
up its canons on the basis of a fixed zodiac commonly known
as the Nirayana system. The effect of this will be clear
from the following example.

The winter season (ki&ira) begins on the winter solstice-
day which date is also marked in all the Siddhdntas by
sun's entry (safnkranti) into Makara. This event occurs on
the 22nd December. But the Indian calendar makers,
following the nirayana system, state that the Makara
Safnkranti happens not on the 22nd December but on the
14th January and the winter season also begins on that
date. Similar is the case with other seasons also. The result
is that there is a* clear difference of 23 days in the reckoning
of seasons. The later Hindu savants tried to reconcile the
two points of view by adopting a theory of trepidation,
which after Newton's explanation of precession, has been
definitely shown to be false. It is therefore absolutely
wrong to stick to the nirayana system.

It is however refreshing to tfnd that a few Indian
savants have definitely stood against the false nirayana
system. The earliest were MuSjala Bha^a (932 A.D.), a
South Indian astronomer and Prthudaka Svami (950 A.D.),
who observed at Kuruksetra. One of the latest was Mm.
Bapudev Sastri, 0. I. R, Professor in the Sanskrit College,
Banaras, who wrote in 1862, as follows :

"Since the nirayana safnkrantis cannot be determined
with precision and without doubt and since the nirayana
raiis have no bearing on the ecliptic and its northern and
southern halves, we must not hanker after nirayana system
for the purposes of our religious and other rites. We must
accept say ana and our religious and other rites should be
performed in accordance with the say ana .system".

0. R. -41

259

260

REPORT OF THE CALENDAR REFORM COMMITTEE

It is not generally known that another great man who
probably felt that the nirayaria system gave us wrong
seasons, was Pandit Ishwar Chandra Vidyasagar. We
learn from his biography that he had a course in Indian
astronomy while he was a student of the Sanskrit College,
Calcutta about 1840. Before him, the Vasanta r Spring
insisted of the months Madhu and Madhava, i.e., Caitra
and Vai&akha, as in other parts of India. But from 1850,
Vidyasagar began to bring out text books in Bengali in
which he retarded the seasons by a month, e.g., he said that
the spring consists of Phalguna and Caitra, and no one
questioned it. So in Bengal, as far as popular notion goes,
Vasanta season starts on Feb. 12, while in other parts it
starts on March 14, a month later, while the correct
astronomical date according to Hindu Siddhantas is Feb. 19.
Bengal thus commits a negative mistake of 7 days while
other parts of India has a positive mistake of 23 days.

The position in respect of all the seasons is stated
below :

Sun's longitude Correct date Present date

Vasanta ( - ) 30° to 30° Feb. 19 to Apr. 19 Mar. 14 to May 13
(Spring)

Grisma 30° to 90° Apr. 20 to June 20 May 14 to July 15
(Summer)

Varsa 90° to 150° June 21 to Aug. 22 July 16 to Sep. 15
(Rains)

Sarat 150° to 210° Aug. 23 to Oct. 22 Sep. 16 to Nov. 15
( Autumn)

Hemanta 210° to 270° Oct. 23 to Dec. 21 Nov. 16 to Jan. 12
(Late Autumn)

Sisira 270° to 330° Dec. 22 to Feb. 18 Jan. 13 to Mar. 14
(Winter)

In continuing to follow the nirayana system, the Hindu
calendar makers are under delusion that they are following
the path of Dharma. They are aerially committing the
whole Hindu society to Adharma.

The period covering the north-ward journey of the sun
was known in Indian astronomy as the UttarayaT^a
i.e., north- ward passage and it consisted of the Winter,
Spring and Summer. It is the period from winter solstice
to summer solstice, and vice-versa, the period from summer
solstice to winter solstice was known as the Daksii^ayana,
i.e., southward passage and it consisted of Rains, Autumn
and Hemanta.

The names of months given in the second column of
Table No. 28 are found first in Taittiriya Safnhita, and they
are tropical, because they attempt to define the physical
characteristics of the months.

Madhu means. 'Honey' and the name indicates

that the month was pleasant like honey.

Madhava... means - Honey like' or 'Sweet one'.

The names are thus expressive of the pleasantness of the
spring season.

The figures in the third column of the table below denote
the angular distance of the sun from the astronomical first
point of Aries (the V.E. point) indicating the beginning of
the month.

The two months constituting the 'Spring Season' would
thus include the day from Feb. 19 or 20 to April 19 or 20.
The Vernal Equinox day (March 21) would be just in the
middle. The same is the case with other seasons each of
two months.

Spring

Summer

Rains

Autumn

Late Autumn!

Winter

Madhu
Madhava

Sukra
l^uci

Nabhas
Nabbasya

Isa
Urja

Sahas
Sahasya

Tapas
Tapasya

Table 28.

1 -30°

J o

1 30

J 60

) 90
J 120

1 150
J 180

\ 210
f 240

Honey or sweet spring
The sweet one

Illuminating
Burning

Cloud
Cloudy

Moisture
Force

Power
Powerful

270 Penance, mortification,
fire

300 Pain (produced by heat)

These names were seldom used by the common people,
but they were very popular with poets.

The figures in the second column of table No. 29
denote the angular distance of the sun on the ecliptic, the
origin being the first point of Aries, We have described
in § 4.5 how an idea of the ecliptic was derived from night
observations of the sky and observation of eclipses, and
how it came to be used as a reference plane from very
ancient times.

The Indian definition of the seasons, though was based
on the cardinal days, was different from the definition of the
westerners who divided the year into four seasons each of
three months Winter, Spring, Summer and Autumn, starting
from*the four cardinal days. The ancient Indians divided
the year into six seasons each of two months as given in
the table below. The spring season did not start with the
vernal equinox, as already stated but a month earlier and it
was extended a month later, and so for every season.

Table 29.

Indian Seasons Tropical Month-names Lunar Month-names

Spring (-30° to 30°)
Summer (30° to 90°)
RainB (90° to 150°)
Autumn (150P to 210°)
Late Autumn

(210 5 to27(P)
Winter (270°to330e)

Madhu & Madhava
&ukra & f§uci
Nabhas & Nabhasya
Isa & Orja

Sahas & Sahasya
Tapas & Tapasya

Caitra- Vaisfikha
Jyaig^ha- Agatha
Sravana-Bhadra
Asvina-Kartika

Agrahayana-Pausa
Magha-Phalguna

The early Greek astronomers have left records about
their successive attempts to measure the length of the year

INDIAN CALENDAK

261

correctly. It is now known that they all used the gnomon.
Measures of the length of the different seasons and of the
year by some of their eminent astronomers are 'given in the
table (No. 30) below.

The Chaldeans must have also measured ' the length ot
the year by the same method, either somewhat earlier or
simultaneously with the early Greeks, but their names,
excepting those of a few have not survived. But if in
reality, the nineteen-year cycle was of. as early as 747 B.C.,
they must have arrived at a correct length of the year much
earlier than any other nation.

The Length of the Seasons : The lengths of seasons were
found exactly in the same way as in the case of the
year, e.g.> in the case of Spring, by counting the number of
days from the day next to the yernal equinox day to the
summer solstice day. The number would be variable from
year t6 year, but a correct value was found by taking the
observations for a number of years and taking the mean.
The lengths obtained by early astronomers are :

Table 30.

Spring Summer Autumn Winter Total
days days days days days
Chaldean ... 94.50 92.73 88.59 89.44 365,26

Euctemon(432B.C) 93 90 90 92 365

Calippos (370B.C) 94 92 89 90 365

Correct values

for 1384 B.C. ... 94.09 91.29 88.58 91.29 365.25
The ancients early discovered that the seasons were of
unequal length, but they were ignorant of the physical
reasons. These exact definitions of seasons, both in India
and in the West, were arrived at very early, and are very
important for accurate calendar-making ; but the true
meaning of these definitions were forgotten in the succeed-
ing periods in India.

In European astronomy, which is derived from Graeco-
Chaldean astronomy, we have :

Spring 0°— 90° from V.E. to S.S.

Summer 90°— 180° " S.S. to A.E.
Autumn 180°— 270° " A.E. to W.S.
Winter 270°— 360° " W.S. to V.B.
According to this scheme, the Bainy season consisting
of months of Nabhas and Nabhasya formally set in when

the sun crossed the summer solstice (June 22), as is evident
from the lines in Kalidasa's MeghadUta or Cloud-Messenger.

Pratyasanne Nabhasi dayitajivita lambanarthi
Jimutena svakusalamayim harayi^yan pravrttim.

Translation : When the month of Nabhas was imminent,
( just marking the onset of monsoon ), etc.**

Or in the Bamayana, Ayodhyakay><ia

Udaggatva-abhyupabrtte paretacaritam disam
Abrnvana disab sarvat snigdha dadrsire ghanah.

Translation : When the sun just reversed its motion after
going (continuously) to the north, and began to proceed in
the direction inhabited by departed souls (dak?inayana), the
whole sky was overcast with clouds (i.e., the monsoon set
in);.-..

WiDter solstice set in with the month of Tapas, - which
means penance. The winter solstice as mentioned above
was the time from which the yearly sacrifices started.

The month names in the last column of table (No. 29)
are 'lunar', but they were linked to the solar months. They
are now in universal use all over India to denote
solar as well as lunar months ; but the two varieties are
distinguished by the adjectives 'Solar' or 'Lunar*.

Both the European and Indian definitions of seasons
are scientific as they are based on the cardinal days. The
difference in nomenclature is trivial.

The Length of the Year : The length of the year, as
mentioned earlier, must have been found by counting the
number of days from one equinox to another, or one solstice
to another.

In actual practice, the number of days of the year,
counted in this way would vary between 365 and 366. In
the early stages, the length of the year was whole-numbered,
but Indians of Vedanga Jyotisa period had a year of : 366
days. Later when they came to a rigorous definition of the
year, they realized that the number of days was not whole,
but involved fractions. Probably the attempt at determin-
ing the exact length of the year involving fractional
numbers was obtained by adding up the lengths for a
number of years, and taking the mean.

APPENDIX 5-B

The Zero-point of the Hindu Zodiae

The Zero-point of the Hindu Zodiac : By this is meant
the Vernal Equinoctial Point (first point of Aries) at the
time when the Hindu savants switched on from the old
Vedaiiga-Jyoti$a calendar to the Siddhantic calendar (let
us eel this the epoch of the Siddhanta- Jyotisa or S. J.).
There is a wide spread belief that a definite location can be
found for this point from the data given in the Surya-
Siddhanta and other standard treatises. This impression is
however wrong.

Its location has to be inferred from the co-ordinates
given for known stars in Chap. VIII of the SUrya Siddhanta.
From these data Diksit thought that he had proved that it
was very close to Bevati (C Piscium) ; but another school
thinks that the autumnal equinoctial point (first point of
Libra) at this epoch was very close to the star Citra (Spica,
< Virginis), and therefore the first point of Aries at the
epoch of S.J was 180° behind this point. The celestial
longitude in 1950 of f Piscium was 19° 10' 39" and of
* Virginis was 203° 8' 36". The longitudes of the first
point of Aries, according to the two schools therefore
differ by 23° 9'(-)l9° 11'= 3° 58' and they cannot be
identical. Bevati or f Piscium was closest to T (the V.E.
point) about 575 A.D., and Citra or < Virginis was closest
to ^ (the A.E. point) about 285 A.D., a clear difference
of 290 years.

Thus even those who uphold the nirayarta school are
not agreed amongst themselves regarding the exact location
of the vernal point in the age of the Sftrya-Siddh&nta
and though they talk of the Hindu zero-point, they do
not know where it is. Still such is the intoxication
for partisanship that for 50 years, a wordy warfare
regarding the adoption of either of these two points as the
zero-point of the Hindu zodiac has gone on between the
two rival factions known respectively as the Bevafl-Pak§a
and Citr3,-Pak$a, but as we shall show the different parties
are simply beating about the bush for nothing.

Chapter VIII of the S.S gives a table of the celestial co-
ordinates (Dhruvaka and Vik$epa) of the junction-stars
(identifying stars) of 27 asterisms forming the Hindu lunar
zodiac. It is agreed by all that these co-ordinates must

have been given taking the position of the V.E. point at the
observer's time as. the fiducial point. It is possible to
locate it, as Burgess had shown in his edition of the S.S., if
with the aid of the data given, X, i.e., celestial longitude of
the junction- stars in the epoch of S.J. is calculated, and
compare it with the X of the same stars for 1950. Let the
two values of X be denoted by \± and X a , \ x being the value
at the epoch of S. J., X t for the year 1950. ThenX a -X x
should have a constant value, which is the celestial
longitude of the V.E. point at the epoch of the S.J. on the
assumption that they refer to observations at a definite
point of time. The following is a short exposition of
Burgess's calculations.

The S.S. gives the position of the junction-stars in
terms of Dhruvaka and Vik$epa, two co-ordinates peculiar
to Sury a- Siddhanta. Their meaning and relation to the
usually adopted co-ordinates is illustrated by means of
fig, 27 and for convenience of the reader, the standard

Kg. 27

designations, symbolisms used for the different systems of
celestial co-ordinates along with their Hindu equivalents
are shown in the table below :

Table 31 — Siddhantic designation of celestial co-ordinates.

Co-ordinate

Hindu

Symbol

Figure

Bemarks

Designation

Celestial longitude

Bhoga

As in Surya Siddhanta

Celestial latitude

$ara

Used by Bhaskara

Eight Ascension

Visuvarhsa

Modern

Declination

Kranti

As in Surya Siddhanta

Polar longitude

Dhruvaka

Polar latitude

Viksepa

262

INDIAN CALENDAR

263

With the aid of spherical trigonometry, the following
relations may be deduced : —

sin £ = sin d sin B ...(l)

sm (X— I)— tan j8 cot B \ ((X \
or tan (X-l)=tan d cos B J KA)
where, cot \B=cos I tan « (3)

The objective is to deduce the values of X and j8 of a
star whose Z, d are to be found from Chap. VIII of S.S.
As the formulae show, the key angle is B, which is deter-
mined with the aid of relation (3). Then (l) gives us j3
and (2) gives us X— I. So X and J8 for the star are found.

Proceeding in this way, Burgess calculated the values
of X and of the junction-stars given in the S.S. We have
•hacked these calculations. These are reproduced in table
No. 32 on pp. 264-65 in which :

Column 1 gives us the serial no. of the naksatra.

* 2 " their names.

* 3 " " the name of the junction star as

accepted ( see however later
remarks).

m 4 " " the magnitude of the star.

" 6 " " the celestial longitude of the star

in 1950 from data given in a
modern Ephemeris.
6 " the celestial latitude of the star.

* 7 " " the dhruvaka or polar longitude

as given in S.S.
" 8 " " viksepa or polar latitude as given

in S.S.

" 9 »* " the celestial longitude of junction

star, from the data given in the
S.S. converted with the aid of
the formula mentioned above.
. " 10 " " celestial latitude similarly conver-
ted from data given in S.S.

" 11 " " the difference in celestial longitude

of the star for 1950 over that
for the time of S3.

" 12- " " the difference between the lati-
tudes.

It iB evident that 0-/3' ought to be zero for all stars,
which is however not the fact as may be seen from the
table. In the time of the S.S., the observations cannot be
expected to have been very precise. But yet we cannot
probably hold that an identification is correct when the
difference is too large. We are therefore rejecting all
identifications where j8 — 0' exceeds 2°. Probably these stars
have not been correctly identified from the description
given for them, or the co-ordinates given in the Surya-
Siddh&nta were erroneously determined or wrongly handed
down to us. In the case of other stars, we find that X a — X x
is 16° 47' (or 10° 52'), 16° 58' and 26 u ' 18' for three stars.
We are also rejecting these three identifications. This
leaves us with the identification of 16 stars as somewhat

certain. The values of X a — Xi are in three groups as
follows :

Group 1.

No X.— Xi

-.2 22° 53'

8 22 1

9 22 57

14 22 21

Group 2.

.21

.20

16
10

4 20 57

21 21

Group 3.

..7
18
20
22
27

20 8

20 47
18
2

19 40

18 58

Average

1-22° 33'

}

h 20° 48'

19
18

14
34

19 21

h 19° 9'

(N.B. In giving the Dhruvaka and Viksepa, the S.S.
uses a unit called Liptika, which means a minute of arc.
This is traced to Greek "Lepton'*. Prof, B. V. Vaidya
thinks that some of the figures for asterisms, as they are
given by cryptic Sanskrit words, have not been properly
interpreted).

We are not aware how the Hindu savants determined
the dhruvakas and vik§epas. It appears that they had a
kind of armillary sphere with an ecliptic circle which they
used to set to the ecliptic with the aid of standard stars
like Pu$ya (S Gancri), Magha {<Leonis) Citra (< Virgin**},
Visakha {< Libra) and l^atabhisaj (\AquaHi) and BevatI
it Piscium). They could also calculate the dhruvaka and
viksepa of a star during the moment of its transit over the
meridian of the place of observation. They calculated the
daiama lagna ("known as the tenth house in astrological
parlour) for the moment of transit from tables already
constructed for the latitude of the observer, and this daiama
lagna was the required dhruvaka of the star. By using
two big vertical poles (i.e., gnomons) situated in the north-
south line, the zenith distance of the star at transit could
be determined from which the declination of the star was
deduced, from the relation :

Declination = latitude of place minus zenith distance.

Since Viksepa (BS) = QS-QB i.e., declination of the
star minus declination of a point B on the ecliptic [which
is sin- x (sin I sin «)], the polar longitude (dhruvaka) and the
declination give the viksepa which is thus :
S — sin'^sin I sin «)

Anyhow the above analysis seems to show that the
co-ordinates of stars were determined at different epochs.
Firstly when T was respectively 22° 21' ahead of the
present T , secondly when it was 20° 8' ahead, and
thirdly when it was 19° 21 ' ahead. The epochs come out
to be 340 A.D., 500 A.D., and 560 A.D., respectively.
The first epoch is nearly 200 years from the time of
Ptolemy, and if it is assumed that Hindu astronomers
assumed Citra (Spica or < Virginia) to occupy the first point

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BEPORT OF THE CALENDAR REFORM COMMITTEE

of Bibra, the epoch comes out to be 285 A.D., and the
corresponding Vernal point 2° to the west of Ptolemy's.

This analysis shows that the Indian astronomers had
arrived at the idea that the equinoctial point should he
properly located with reference to some standard stars and
there were probably three attempts, one about 285 A.D.,
the next about 500 A.D., and the last one about 570 A.D.
They had not accepted the first point given by Ptolemy or
any western astronomer.

The compiler (or compilers) of the S.S. was clearly
unconscious of the precession of equinoxes, and while in his
report, he made a selection of these data, he did not perceive
that they were inconsistent with the idea of a fixed V.E, point.

But he did not err on the fundamental point. He had
clearly laid down that Mesadi, i.e., the first point of Aries
from which the year was to be started was to be identified
with the vernal equinoctial point.

It is to be noticed that though the maker of the S.S. has
absorbed many of the ideas from Greek astronomy including
the use of technical terms like hora, liptikd, kendra, etc., he
did not either blindly copy the Graeco -Chaldean data. From
whichever source he might have got the ideas, he absorbed
it correctly and made an attempt to fix up the actual V.K
point, as required in Chaldean astronomy, otherwise his
zero-point would have been coincident with Ptolemy's.
We have shown that whatever the Hindu zero-point of the
zodiac might be, it is not coincident with that of Ptolemy.

APPENDIX 5-C

Gnomon Measurements in the Aitareya Brahmaaa

References to the observation of the solstice are found
in very early literature as the following passage from the
Aitareya Brdhmana shows :

'They perform the Ekavimsa day, the Vi^uvan^ in the
middle of the year : by this EkavimU day the gods raised
up the sun towards the world of heaven (the highest region
of the heavens, viz., the zenith). Eor this reason , this sun
(as raised up) is (called) Ekavimsa, of this Ekavimsa sun
(or the day), the ten days before are ordained for the
hymns to be chanted during the day ; the ten days after
are also ordained in the same way ; in the middle lies the'
Ekavimsa established on both sides in the Viraj (a period
of ten days). It is certainly established in the Virdj.
Therefore he going between (the two periods of 10 days)
over these worlds, does not waver.'

'The gods were afraid of this Aditya (the sun) falling
from this world of heaven (the highest place in the
heavens) ; him with three worlds (diurnal circles) of heaven
(in the heavens) from below they propped up ; the Stomas
are the three worlds of heaven (diurnal circles in the
heavens). They were also afraid of his falling away
upward ; him with three worlds of heaven (diurnal circles
in the heavens) from above they propped up ; the Stomas
are the three worlds of heaven (diurnal circles in the
heavens) indeed. Thus three below are the Saptadasas
(seventeen), three above ; in the middle is the EkavifnSa
on both sides supported by Svarasamans. Therefore he
going between these Svarasamans over these worlds does
not waver*.

This obscure passage has been interpreted as follows
by Prof. P.C. Sengupta in his Ancient Indian Chronology.

The Vedic year-long sacrifices were begun in the earliest
times on the day following the winter solstice. Hence the
Visuvan which means the middle day of the year was the
summer solstice day. The above passage shows that the
sun was observed by the Vedic Hindus to remain stationary
1 e., without any change in the merdian zenith distance
for 21 days near the summer solstice. The argument was
this that if the sun remained stationary for 21 days, he
must have had 10 days of northerly motion, 10 days of
southerly motion, and the middle (eleventh) day was
certainly the day of the summer solstice ; hence the sun
going over these worlds, in the interval between the two
periods of 10 days on either side, did not waver'. Thus
from a rough observation, the Vedic Hindus could find the
real day of the summer or winter solstice.

The next passage from the Aitareya Brahma\ia (not
quoted) divides the Viraj of 10 days thus ; 10 = 6 + 1 + 3-
the first 6 days were set apart for a Sadaha (six day-) period,
followed by an atir&tra or extra day and then came the
three days of the three Stomas or Svarasamans. \The
atiratra days before and after the solstice day were
respectively styled Abhijit and Visvajit days. It may thus
be inferred that the Vedic Hindus by more accurate
observation found later on that the sun remained stationary
at the summer solstice for 7 and not 21 days.

Question may now be asked how could they observe fchat
the sun remained stationary for 21 days and not for
23, 27, 29, or 31 days. This depended on the degree of
accuracy of observation possible for the Vedic Hindus by
their methods of measurement. They probably observed
the noon-shadow of a vertical pole.

APPENDIX 5-D

Precession of the Equinoxes amongst
Indian Astronomers

On p. 226, we have given references to pre-Siddhantic
notices of the location of the vernal point in the sky. We
saw that ancient Indian savants noticed its gradual shift
( due to precession ), but were only puzzled by the pheno-
menon. Let us see what was the experience of the
Siddhantic astronomers in this respect.

Dlksit, in his Bharatiya Jyolisastra, has summarized the-
adventures of the idea of Preeession of the Equinoxes
amongst Indian astronomers of the Siddhanta period. The
following account draws heavily on his Chap. 3 ( p. 326 ) on
Ai/ana-Calana, which literally means 'the movement of the
solstitial points'. *

The 'Solstitial points' were known amongst Indians as
'Ayanas' anth Siddhantic astronomers regarded them as
'imaginary planets' as they used to do in the case of the
nodes of the lunar orbit. Though the nomenclature is cum-
brous, the chapter actually deals with the precession of
the equinoxes, as this point is 90° behind the summer
solstitial point.

Before the Siddhantic period, the lunar calendar was of
primary importance, hence the exact fixation of the vernal
equinoctial point ( T Q ) was not very important. It became
important from the time the Indian astronomers of the
Siddhanta period first realized that T Q should form the
zero-point of the zodiac ; and made attempts at different
epochs ( 285 A.D.-600 A.D. ) to give co-ordinates of stars
(Dhruvaka and Vik$epa) with respect to this as the initial
point. Chapter VIII of modern SUrya- Siddhanta gijves a
resume' of these co-ordinates for, the junction-stars of the
lunar asterisms. Our analysis of these data as given in
Appendix 5-B shows that these co-ordinates must have
been obtained by actual observations at different epochs, and
as the compiler of the SUry a- Siddhanta was ignorant of the
phenomenon of precession of the equinoxes, he made an
uncritical selection of these data compiled at different times
and included them in his Chap. VIII.

From these data, it is impossible to determine the exact
location of T at the time when the SUry a- Siddhanta was
complied. So the wordy warfare between the upholders of
the Citra-pak$a and the Bevati-pak$a becomes meaningless
as pointed out on p. 262.

* The word l Ayana Galana* strictly means the movement of the
"Solstitial Points". Bhaskaracarya uses the word 'Sampat-Galcma'
for movement of the equinoctial points ( T and £t ). Mathematically
the two denominations are equivalent, but it has become the practice
in Hindu astronomy to render the term 'Precession of the Equinoxes'
by the words 'Ayana Calana*. We shall follow this practice through-
out.

The surmise that the early Siddhantic astronomers were
ignorant of the movement of the equinoxes is supported by
the fact that neither of the early eminent astronomers
Aryabhata I (476 — 523 A.D.) nor Lalla (748 A.D.) whose
dates are known, mention anything about precession of the
equinoxes in their writings which have come down to us.
If they derived their knowledge of astronomy from the West,
they followed the current western practice of ignoring the
precession. The astronomer Varahamihira, who wrote
about 550 A. D., and has left us a compendium of the five
Siidhantas, makes no mention of the phenomenon. This
proves that the original SUrya SiddhSmta as known to
Varahamihira contained no reference" to the movement of
the equinoctial points. In his Bfhat SaUhita as mentioned
on p. 226, Varahamihira, however, noted that the solstices
were receding back, but he could not say anything about the
actual nature of the precession or assign any rate to it.

But it is obvious that once the Indian astronomers
recognized T as the starting point of the zodiac, and started
giving co-ordinates of stars in terms of T Q as the starting
point, they could not avoid noticing the movement of the
equinoxes, just as it happened with Hipparchos in Greece.
According to Brahmagupta (628 A.D.), the first astronomer
who made a pointed reference to it was one Visnu Candra
author of the Vasitfha Siddhanta whose date is given as'
ca. 578 A.D. He was supported by one &isena of whom
only the name survives. For holding these views these
astronomers were roundly abused by Brahmagupta whose
views on these points appear to have been confused. But
undeterred by the great prestige of Brahmagupta, later
astronomers continued to make references to the movement
of the equinoctial points.

We cite some examples.

MuSjala Bhata, a south Indian astronomer, wrote a
treatise called Laghumanasa in 854 $aka or 932 A.D. A
later commentator, Munisvara, ascribes the following
verses to him.

Uttarato yamyadisam yamyantattadanu

saumyadigbhagam
parisaratam gaganasadam calanam kincid bhave-

dapame. 1.

Visuvadapakramamandala-sampate praci mesadih
pascattula^iranayo-rapakramasambhavat proktafc. 2.
Basitrayantaresmat karkadiranukramanmrgadisca
tatra ca parama krantirjinabhagamitatha tatraiva. 3
NirdiB^o-yanasandhiscalanam tatraiva sambhavati
tadbhaganab kalpe syu-go-rasa-rasago-'nka-candra

mitatu 4.

C.R.— 42

267

268

REPORT of the oalendab reform committee

Translation

1. While the celestial bodies move in the sky from
north to south and again from south to north, a very small
variation takes place in their declination.

2. The (ascending) node in which the celestial equator
and the ecliptic intersect is the first point of Aries (Me§idi\
and it gives the 'East'. The second node is the first point
of Libra (Tuladi), and these two points never change their
-declination value (which is zero).

3. The first point of Cancer (KarkZdi) is at a distance
oi three signs (i.e. 90°) from it, and at a distance of three
signs in the reverse order is the position of the first point of
Capricorn (Makaradi), These give the positions of maximum
declination which is 24 degrees.

4. The solstitial points (which mark the ayanas) show
a movement, and the number of their revolutions in a Kalpa
is counted as 199669.

The last passage recognizes processional motion, says
that it is continuous, and gives^the rate as 59".9 per year.
Munjala Bhata makes no mention of trepidation. He noticed
that the Ayanas had processed by about 6° from the position
given in the Surya-Sidtlh&nta.

Prthudaka Svami (born 928 A.D.), an astronomer who
observed at Peihowa, near Kuruksetra, commenting on a
passage of Brahmagupta says :

"The revolution of Ay ana in one Kalpa is 189411.
This is called the Ayana Yugd".
This passage recognizes the continuous nature of
precessional motion, and gives the rate of processional
motion as 56".82 seconds per year.

So far we have no mention of the 'Theory of Trepidation'
This is first mentioned in the Arya Siddhanta t ascribed to
Aryabhata II, whose date is 1028 A.D. It says :
Ayanagrahadot krantijyacapam kendravat dhanarnam syat
Ayanalavastat samskrta khetadayana carapamalagnani. 12.

Translation : — Find the sine declination {krantijya) of
the ayanagraha (in a way similar to that of the sun's
declination) ; from it deduce the amount of declination,
plus (north) or minus (south), which is the amount of
ayanafnsa* After applying this ayanafn§a-corToction to
the planet, the values of cava (half the difference between
the lengths of day and night), declination of planets, lagna
(the orient ecliptic point), etc., are to be calculated.

This has been interpreted as follows (Dlkgit, p.330).

The equinox oscillates between ±24°, and the number of
revolutions of the Ayana-pl&Tiet in a Kalpa is 578159, which
gives the period of revolution as 7472 years and the annual
rate of motion as 173 "A. During a quarter period viz,, 1868
years, the ayanafn§a increases from 0° to 24°, at first,
rapidly, then gradually more slowly like the increase of

* This is a technical term used by Indian astronomers to denote
the distance of the vernal point from the fixed Hindu Zodiac,

declination of the sun. Thereafter it diminishes in like
manner and after the lapse of 3736 years, i.e. the half period,
it again becomes zero and goes on the other side. The annual
rate of motion, which on the average amounts to 46 .3
seconds, varies fromzfc 70"*5 to '

We now come to a very controversial passage in the
modern SUrya Siddkcinta, Chap. Ill, verses 9 to 12.
These are :

Trimsat krtyo yuge bhanarii cakrarii prak parilamvate
tadgunad bhudinairbhaktat dyuganat yadabapyate. 9
Taddostrighna dasaptamsa vijtieya ayanabhidhat
tatsamskrtadgrahat kranticohaya caradaiadikam
sphutam drktulyatam gacchedayane visuvadvaye. 10
Prak cakram calitam hine chayarkat karanagate
antaramsai rathavrtya pascacchesaistathadhike. 11
Evaih visuvaticchaya svadese ya dinardhaja
dak^inottara rekhayaih sa tatra visuvat prabha. 12
Translation

9. In an Age [yuga\ the circle of the asterisms (bha)
falls back eastward thirty score of revolutions. Of the
result obtained after multiplying the sum of days (dyugatya)
by this number, and dividing by the number of natural
days in an Age,

10. Take the part which determines the sine, multiply
it by three, and divide by ten ; thus are found the degrees
called those of the precession (ayana). From the longitude
of a planet as corrected by these are to be calculated the
declination, shadow, ascensional difference (caradala) etc.

11. The circle, as thus corrected, accords with its ob-
served place at the solstice (ayana) and at either equinox ; it
has moved eastward, when the longitude of the sun, as obtain-
ed by calculation, is less than that derived from the shadow.

12. By the number of degrees of the difference ; then,
turning back, it has moved westward by the amount of
difference, when calculated longitude is greater.

These verses occur in the chapter on astronomical
measurements by the gnomon, and are misfits there ;
according to all authorities, these verses did not exist in the
original SUrya-Siddhanta, but have been extrapolated there,
and have no reference to the context of the chapter. The
extrapolation must, however, have taken place before the
time of Bhaskaracarya II (1114-1178 A.D.), because he
comments on this passage.

The passage supports the theory of trepidation and says
that the amplitude of precessional oscillation is 27° and the
period of one complete oscillation is stated to be 7200 years.
The rate of precession is given as 54" per year, which is
uniform and the same throughout the oscillation. These
stanzas are quoted by Indian astrologers who are advocates
of the nirayana system, in support of their arguments for
sticking to the sidereal year. They say that the present
ayanafnia is about 22°, and T will go on processing for
another 350 years till ayan&?ri§a becomes 27° and will" then,
turn back on its return journey.

INDIAN CALENDAR

269

This is sufficient argument to them to turn down all
proposals lor S&yana reckoning taking the length of the
year to be tropical.

We now take the opinion of the last great Indian
astronomer Bhaskaracarya II (1150 A.D.).

He uses the term * Sampat-Calana* i.e., movement of the
intersection of the ecliptic and the equator, instead of the
classical term Ayana. He says :

Siddhanta &iromani f Goladliyaya,
Golabandhadfii k&ra

Tasya [visuvatkrantivalayapatasya] api calanamasti.
Ye'ayanacalana bhagah prasiddhasta eva vilomagasya

krantipatasya bhagah

TranslatiXm : — It (the equinox) has also movement.
What is commonly known as the amount of precession
(ayanafn&a) is the same as the longitude of the equinoctial
point measured backwards.

This evidently shows that he regarded the change as due
to the retrograde motion of the node (i.e. equinoctial point)
like modern European astronomers.

He criticises Brahmagupta for his views on Ayana
Calana and says : "One can observe that at the time of
Brahmagupta, the ayanain&a value was very small and
hence it is likely that it could not have come to his notice ;
yet how is it that he did not take the rate of revolution of
equinoxes as given by the Sury a- Siddhanta, just as he has
taken figures for rates in some other cases on the basis (or
authority) of already proved and accepted rates".

He further says :

Ayanacalanam yaduktam Munjaladyaib sa evayam

(krantipatab)

tatpakse tadbhaganafr kalpe go'ngartu-nanda-go-candrah

(199669;.

Atha ca ye va te va bhaganah bhavantu yada ye'msa
nipunairupa labhyante tada sa eva krantipatab-

Translation : — "What Munjala and others have mention-
ed as Ayana Calana 1 ', is nothing but the motion of this
equinoctial point. According to their view the number of
revolution in a Kalpa is 199669 (yielding annul rate of
59".9). Let whatsoever be the number of revolutions,
whatever amount is obtained by expert observers is the
angle of precession for that time."

From this it is clear that he recommends one to accept
the ayanafnia which one would actually get by observation
of sun's place at any particular time. Dlksit says :

I have not come across single statement in which
Bhaskaracarya has clearly said that equinoctial point makes
a complete "circular revolution", nor does be say that "it
does not make it".

He has taken 1 minute per year as the ayana-motion
and has supposed 11° as th« ayandlh&a in l^aka 1105. He
thus means to take Saka 445 as the zero-precession year.

We thus perceive that Indian astronomers up to the time
of Bhaskaracarya were as much divided in their ideas about
precesssion of the equinoxes as the contemporary Arab
astronomers of the West (Hispano- Muslim), and the East.
It is only after 1024 A.D. that they adopted a theory of
trepidation. The earlier-astronomers like Munjala and
Prthudaka merely noticed precession and gave their own
rates for it. Bhaskaracarya is non-committal about
trepidation. The Indian astronomers do not appear to have
been influenced by the views of the western astronomers,
the earlier Greeks or later Arabs.

It will be sheer stupidity to hold to the theory of
trepidation of equinoxes 270 years after it has been definitely*
proved to be wrong. The law of universal gravitation will
not be changed by God Almighty to oblige astrologers.

APPENDIX 5-E

The Jovian Years

{Barhaspatya Var§a)

The sidereal period of Jupiter, according to the SUrya
Siddhanta is 4332.32 days which is nearly 11.86 sidereal
years. Therefore Jupiter roughly stays for one year in one
zodiacal sign, if we calculate by mean motion.

This was taken advantage of to devise a cycle of 12
Jovian years. If we divide the Sury a- Siddhanta period by
12, we get 361.026721 days which is taken as the length of
a Jovian year. This is 4.232 days Ie3s than the Surya
Siddhanta solar year. So if a Jovian year and an ordinary
solar year begin on the same day, the Jovian year will
begin to fall back, completing a complete retrogression
65

in 85 — solar years, according to the SUrya- Siddhanta.
Ala.

So 85— solar years — 86^^ Jovian years, and one Jovian
2i 1 1 All

year is expunged in every 85^[ years. The expunged year

is called the Kmya year. In actual practice, the interval
between two expunctions is sometimes 85 and sometimes
86 years.

There was indeed at one time a period of 12 Jovian
years, but at some past epoch, a fivefold multiple, a cycle of
60 Jovian years, each with a special name suffixed by the
word 'Saihvatsara', came into use.

The beginning of the Jovian years is determined by the
entry of Jupiter into an Indian sign by mean motion, the
1st, 13th, 25th, 37th and 49th years 'being marked by the
entry of Jupiter into the sign Kumbha, and not Mesa which
is otherwise the first of the signs of the Siddhantas. It
thus appears that the system of counting Jovian years is a
pre-Siddhilntic practice

The sixty-year cycle is at present'in daily use in Southern
India (south of Narmada) where each year (the solar year or
the luni-solar year) is named after that of the corresponding
Jovian year. The years are counted there in regular succes-
sion and no safnvatsara is expunged. This practice is being
followed since about 905-06 A.D. (827 Saka), as a result of
which the number of Northtlndian Safnvatsara has been
gradually gaining over that of the South from that time.
The Saka year 1876 (1954-55 A.D.) is named 41 Plavanga
in the North while in the South it is 28 Jaya.

The following are the names of the different years ;

(1)

Prabhava

(21) Sarvajit

(41) Plavanga

(2)

Vibhava

(22) Sarvadharin (42) Kilaka

(3)

Sukla

(23) Virodhin

(43) Saumya

(4)

Pramoda

(24) Vikrta

(44) Sadharana

(5)

Prajapati

(25) Khara

(45) Virodhakrfc

(6)

Angiras

(26) Nandana

(46) Paridhavin

(7)

Srimukha

(27) Vijaya

(47) Pramadin

(8)

Bhava

(28) Jaya

(48) Ananda

(9)

Yuvan

(29) Manmatha

(49) Kuksasa

(10)

Dhatri

(30) Durmukha

(50) Anala (Nala)

(11)

Isvara

(31) Hemalamba

(51) Pingala

(12)

Bahudhanya

(32) Yilamba

(52) Kalayukfca

(13)

Pramathin

(33) Vikarin

(53) Siddharthin

(14)

Vikrama

(34) ^arvarl

(54) Eaudra

(15)

Vrsa

(35) Plava

(55) Durmati

(16)

Chitrabhanu

(36) Subhakrt

(56) Dundubhi

(17)

Subhanu

(37) ^obhana

(57) Rudhirodgarin

(18)

Tarana

(38) Krodhin

(58) Baktaksa

(19)

Parthiva

(39) Visvavasu

(59) Krodhana

(20)

Vyaya

(40) Parabhava

(60) Ksaya (Aksaya)

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INDEX

Abbe Mastrofini, 171

Abd al-Rahaman al-Ruff, 206

Achelis, Miss Elisabeth, 12, 171

Adar, 179

Addaru, 175,176

Adhika ( = mala) month, 7, 247, 230
Agni, 210

Ahargana, 9, 11, 101, 102, 163
Ahoratra, 157, 100

Aitarcya BrTihmana, |89, 216, 219, 22], 266
Akber, 1,159, 214, 251
Aksaya ti tiya, 18, 39
Al-BattanT, 204, 200, 240 ;

rate of precession, 206
Alberuni,198,204, 237-;
Al-Bitruji, 206

Alexander of Macedon, 202, 213, 234, 235

Al-Fargham, 206

Almagest, 204, 206, 238, 240

Aloysius LiliuB, 171

Altekar, Prof., 254

Al-Zarquali, 206

Amanta month, 101, 157, 177, 247
Ammonia clock, 32, 159
Anaximander of Miletus, 188, 202 ;

gnomon. 202
Ancient Indian Chronology, 215, 253,-266
Andan (inscription), 233
Antiochus Sorter, 203
Antiochus I, II of Babylon, 228
Anubis, Egyptian god, 164
Anuvatsara, 225

Anyanka Bhlma Deva of Ganga dynasty, 257

Aparabna, 108

Jpastamba Samhita, 218

Aphelion, 242 ; movement of, 243

Apolloniu s of Perga, 203

Ara (inscription), 230

Arachosia, 229, 230
Aranyaka, 214
Archebius of Taxi la, 230
Archimedes of Syracuse, 203
Archytas of Tare n turn, 202
Ardeshir I of Persia, 232
Ardharatrika system, 1, 253,^254
Ariana, Herat regions, 229
Aries (zodiacal sign), 392, 193
Aries, first, point uf , 157, 192, 199, 207, 239, 240,
262, 268 ;

Hipparcho's, 200, 205, 206 ;

movement of 200, 205, 206 ■

position in different times, 200 (fig).

Ptolemy's, 200
Aristaivhos nf Samos, 203
Armellini, 171

Armillary sphere, 199 (fig.), 263
Arsaces of Parthia, 178
Artabanus I of Parthia, 213
Artabanus II of Parthia, 256

Artemidorus of Puskalavati, 230
ArthakUstra of Kautilya, 235, 236
Aruiiodaya, 108

Aryabhata 1, 204, 234, 236, 237, 238, 240, 2c

253, 254, 267
Aryabhata II, 238, 268
Iryabhatlya of Aryabhata, 162 238, 253
Arya Saiigamika, 232
Irya Siddhanta, 1, 214, 251, 268
Arya Vasula, 232
Asokachalla Deva, 256
Asoke, 177, 212, 227, 228, 252
Assouan papyri, 179
Jjitadhyayl, 214
Astrolatry, 235, 236

Astrology, 12. 194, 196, 205, 206, 235, 236, 256
Atharva Sathhita, 217, 218
At harm Veda, 214, 217, 218
Audayika system, 254

August Gompte, French positivist philosopher
171

Augustus, 168

Ayanamsa, 5, 7, 16, 17, 20, 268, 269 ;

amount of acc. to Aryabhata II, 268

amount of fixed, 16, 17

(see also calendar for five years)

definition, 268

rate of, 7

rate of Bhaskaracarya, 269

value of, 7, 17
Ayanas, 267. 268, 269
Azes, 256

Azes I, 230, 233, 256
Azes II, 230, 233, 256
Azilises, 230, 233

Babylon, 225, 226, 228 ; latitude of, 225
Bachhofer, Dr. L., 230, 231, 232
Badami (inscription), 233, 253
Bailey, 253
Balarama, 227
Banerjce, late R. D,, 212
Bentley, 253

BeroHsus, Chaldean priest, 203
Bharatiya JyotilQstra, 11, 160, 219, 225, 236,
267

Bhaskaracarya, 238, 246, 262, 267, 268, 269 ;

a van a calana, 269
BkCtsmtl 160
Bhattotpala, 237
Bhoga (celestial longitude), 262
Bija (correction), 3
Box lid (inscription), 230
Brahma. Creator in Hindu mythology, 223,

236,238, 239, 240
Brahmagupta, 223, 237, 238, 240, 253, 267, 268,

269

Brahma Siddhanta, 1, 214

Brahmanas, 193, 214, 221, 241, 245
Brahrm, 227, 229, 231, 232, 233
Brhat Samhita, 226, 267
!, Brown, 193

Buddha, 231,235;

nirvana of, 256, 257
views on astrology. 235
Budhagupta, Gupta emperor, 234
Burgess, Rev. E., 238, 253, 262, 263

Calendar, defined, 1, 157 ;
civil, 6 ,

compilation according to S. S., 1 ;
confusion in Indian, 10 ;
Egyptian, 164 ;
French revolution, 167 ;
Fusli, 248 ;

Gregorian, 1, 3, 11, 170-172 ;
Hejira, 1, 166, 179, 180, 214;
history of reform movement, 10, 11 ;
Iranian (Jelali) 1, 166 167 ;
Islamic, 179, 180 ;
Jewish 179 ;
lunar, 3,179, 245,247 ;
luni solar, 1, 3, 174, 249, 251 ; *
calendar in Siddhantas 245-251 ;
of Babylonians, Macedonians, Roma*

and the Jews, 176, 177 ;
principles of 174 ;
Siddhantie rules for 247 ;
National, 12-14 ;
Paitamaha Siddhanta, 223, ;
problems of the, 158, 159 ;
Reformed, 4 ;
Religious 7 ;
Roman, 168 ;

Seleucid Babylonian, 229 ;
Siddhanta Jyotisa period, 245, 246
Solar, 1,2, 164-173, 245;

Siddhanta Jyotisa period, 234-245
Tarikh-i-Jelali, 166, 167 ;
Tarikh-Ilahi, 1, 214, 251, 257, 258 ;
Vedanga Jyotisa, 9, 221, 222, 223 ;
World, 1, 171-173
Calendar of India, Reformed (as recommended
by the Committee), 41-100 ;
explanation of terms used, 40
Calendar Reform,

suggestion received, 5 ;
summary of suggestions, 32-38
Calikya Vallabhesvara, 233
Caliph Omar, 167, 179
Calippos, length of season, 175, 261
Canakya, 213, 235, 236
Cancer, first point of, 192, 199
Candragupta, Maurya, 213, 236, 257
Candragupta II, Vikramiiditya, 254, 255
Capricorn, first point of, 192

273

274

Cara , correction , 268
Cardinal days, 189
Cardinal points, 189, 190, 219;

determination of, 190
Castana, 6aka Satrap, 233, 256
Centauries. 163

Central Station, 3, 4, 7, 14, 40
Chadwick, 202

Chaldean Saras, 184,135, 186,202
Christ, Jesus, 157, 201
Chronometer, 157
Cicero, 205

Cleostratos of Tenedos, 193, 202 ;

zodiac, 193. 202 ;

8-year cycle of intercalation, 202
Clepsydra, 159, 223, 225
Committee, Indian Calendar Reform—

appointment of, 4 ;

dissenting note, 8, 18 ;

final recommendations of civil, 6, 7 ;

final recoromandations of religious, 7, 8 ;

members of, 4 ;

proceedings of the first meeting, 9 ;
proceedings of the second meeting, 15 ;
proceedings of the third meeting, 17 ;
terms of reference. 4
Committee, Indian Ephemeris and Nautical
Almanac, 8

Committee meetings, 4, 5 ; resolutions of 4, o
Compline (division of day), 159
Constantine, Roman emperor, 170
Co-ordinate, celestial, Siddhantic designation
of, 262

Copernicus, 195, 203, 206, 235
Corpus'lnscriptionum Indicantm, 229
Ctujamani yoga, 108
Cunningham, 230, 231
Cycle of Indiction, 162

Dak?inayana, 189. 219, 226, 239, 260
Panda ( = n&4i or ghatika), 160
Darius I, Achemenid emperor, 166, 176, 212,
256

Day,

apparent length of, 226 ;
astronomical, 159 ;
civil, 159 ;
counting of the

succession of, 248 ;
definition of, 157, 217 ;
designation in ancient

time, 183 ;
division among Egyptians, 160 ;
division among Hindus, 160 ;
Julian, 161, 162 ;
length of, 157, 159,259;
length at Babylon, 226 ;
length of longest and shortest, 225 ;
mean solar, 157, 158, 159,197 ;
reckoning of 13, 14 ;
saura, 197 ;
sidereal, 157, 158 ;
solar. 157 ;
starting of, 1 ( 5, 7 ;
sub-divisions of, 159 ;
Debevoise, 230

INDEX

Decad, 164
D' Eglantine, 167
Declination, 192, 204, 263

Demetrius, 213
Democritos of Abdera, 202
I?ewai (inscription), 229
Dkarma Sindhu, 19, 101
Dhruva (celestial pole), 190, 192
Dhruvaka (polar long.), 192, 262, 263, 267

of junction stars, 264, 265
Dlgha NikZya, 235

Diksit, S. B., 11, r9, 160, 212, 219, 223, 224, 225,
236,237,246,262,267.268,269

Diopter, 203

Dios, Macedonian month, 179, 229, 255
Direct motion, 169, 195
Discovery, 190
DurgastamT, 108
Dvadasaha, 217

Earth-
equatorial axis of, 208 ;
period of rotation, 12 ;
polar axis of, 208 ; *
speed in a second, 195 *,
spinning of, 208
Easter, 170, 171
Eclipses-
condition of, 185 ;
list of lunar, 186 ;
list of solar, 187 ;
periodicity of, 185 ;
recurrence of, 186 ;
saros cycle, 184-187 ;
Ecliptic, 158, 181. 191, 192, 197, 198, 207, 259;
definition of, 191 ;
earliest mention of, 199 ;
fixing of, 191 ;
plane Of, 192,207;
pole of, 192,208;
obliquity of, 191,207, 208,225
Ekadasi, observance of, 105
Elements of Euclid, 202
Elliptic theory, 243

Encyclopaedia Britannica, 170, 179, 199
Epagomenai, 164
Ephemerides, 201
Ephemerides Committee, 4, 6
Epicycle, 203
Epigehis, 165

Epiqraphia Indica, 233, 254
Equator, celestial, Ml, 192, 197, 207, 239, 259
Equinoctial days, 188
Equinoxes, 188 ;

autumnal, 189, 192 ;

oscillation of, 268 ;

vernal, 2, 11, 13, 188, 189,192, 205, 253,
260

Era, 13, 177, 228-231, 236, 251, 252, 258 ;
Amli,244,257,258 ;
Arsacid, 178,230;
Azes,232,256;
Bengali San, 257, 258;
Buddha Nirvana, 256-258 ;
Burmese, 162 ;
Cfclukya Vikrama^258 ;
Chedi(KalficurI),258;

Era — eoHtd*

Christian, 170, 251, 258;

current, 251 ;
Diocletion, 162 ;
elapsed, 251 ;
#asli,257,258;
French Revolution, 167 ;
Gahga,257,258;
Gupta, 255, 257,258;
Harsa, 254, 258;
Hojira, 162,180, 258;
introduction of, 177 ;
Jelali (Iranian), 162 ;
Jewish era of Creation, 179 ;
Jezdegerd (Persian), 162 ;
Kalachuri (Chedi), 234 ;
Kaliyuga, 13, 162, 252, 254, 258 ;
Kanaka, 232, 256 ;
Kollam, 257, 258 ;
Kollam Andu, 257 ;
Krta, 254 ;
Kusana.231,232 ;

inscription of, 230 ;
method of date-recording, 232 ;
Laksmana Sena, 258 ;
Laukika kala, 258 ;
Maccabaean, 179 ;
Magi, 258 ;

Mahavira Nirvana, 258 ;
Malavagana, 254 ;
Nabonassar, 162, 177, 178, 253 ;
Newar, 162, 258 ;

Old 6aka, 230, 232-234, 236, 255, 256 ;
Olympiads, 178 ;
Pan«Java kala, 252 ;
Parasurama, 257 ;
Parganati Abda, 257 ;
Parthian, 178, 256 ;
Philippi, 162 ;
Raja 6aka, 258 ;

6aka,2,4,6, 13, 162, 178, 214, 233,234,
236, 255-258 ; earliest records of, 233 ;
Saptar^i, 190, 252, 258 ;
Seleucidean, 161, 176, 178, 179, 229, 230,

231, 255, 256 ;
Vallabhi, 258 ;

Vikrama, 13, 234, 247, 254, 255. 257, 258 ;
Vilayati,244, 257,258;
Yudhist-Mra, 252, 258
Eratosthenes, 178 ; on diameter of the earth,
203

Euclid, 202, 203
Eucratidas, 229

Euctemon, length of season, 175, 261
Eudoxus of Cnidus, 201, 202 ; on geometry , 203
Euphrates, river, 157
Euthydemids, 213
Evection,204

Exact Sciences in Antiquity, 3, 197, 198, 201

Fabricious, 235

Fatehjang (inscription), 229

Festivals, Religious-
Alphabetical list of, 111-115
Christian, 126 ;
general rules for, 101 ;

ft H — 43

INDEX

275

festivals, Religious— eontd.

Lunar—general rules for, 102-105 ;

dates of, 119-124
Moslem, 125;

Solar— general rules for, 106 ;

dates of, 117-118 ;
South Indian— general rules for 106 ;
Fotheringham, Dr. J. K., 165

Galilio, 159

Gandhara, 225, 226, 229, 230 ; latitude of 225
Ganesa caturthT, 108
Oanges, river, 157
Gangooly.P. L.,238
Garga, 226 ; receding of solstices, 226
Garga Samkita, 226
Gargasrota, river, 226
Gauna (mana), 247, 248
Geminus, 197
General Astronomy, 158
Geocentric theory, 204, 239
George Washington, birthday of, 161
Gesh (division of time), 160
Ghatika, 160
Ghirshmnn ) 232
Ginzel, F. K. 162, 193

Gnomon, 159, 174, 188, 189, 202, 219, 223, 268 ;

measure meat in Aitareya Brahman a, 266
Gondophernes, 178, 230
Gorpiaios, Greek month, 231
Great Hear (Sap tarsi), 190
Greek Olympiads, 178
Greenwich time (U. T.), 14
Gregory XIII, Pope, 2, 10, 11, 170, 171
Gunda (inscription), 234
Guptas, 254, 255, 257

Hajj, 180

Hammurabi, Babylonian king, 175

Harappa, 212

Harsa Vardhana, 254

Hashim, Amir AH, 180

Haug, Dr. Martin, 216

Heliacal rising, 164, 191

Heliocentric theory, 203

Herzf eld, 232, 255

Heeiod, 201

Hidda (inscription), 230

Hipparchos of Nicaea, 165, 166, 177, 178, 192,
197, 200, 201, 203, 205, 206, 226, 235,
•237, 240 ;

catalogue of stars, 203 ;
discovery of precession, 205, 267 ;
first point of Aries, 200, 205, 206 ;
geometry & spherical trigonometry, 203,
204

Hippocrates of Chios, 202
History of Science , 206
Hoang Ho, river, 157
Holidays, 5, 6 ; list of, 117-154 ;

Ajmer, 145 ;

Assam, 128 ;

Bhopal,146;

Bihar, 129 ;

Bilaspur, 147 ;

Holidays, list of — contd.
Bombay, 130 ;
Christian festivals, 126 ;
Coorg, 148 ;
Delhi, 149 ;
East Punjab, 134 ;

Fixed holidays & solar festivals, 117, 118 ;

Govt, of India, 127 ;

Himachal Pradesh, 150 ;

Hyderabad, 137 ;

Jammu & Kashmir, 138 ;

Kutch, 151 ;

Lunar festivals, 119-124 ;
Madhya Bharat, 139 ;
Madhya Pradesh, 131 ;
Madras, 132 ;
Manipur, 152 ;
Moslem festivals, 125 ;
Mysore, 140 ;
Orissa, 133 ;

Patiala & East Panjab States Union, 141 ;

Kajasthan, 142 ;

Saurashtra, 143 ;

Travancore-Cochin, 144 ;

Tripura, 153 ;

Uttar Pradesh, 135 ;

Vindhya Pradesh, 154 ;

West Bengal, 136
Hora, 236, 266
Horoscope, 196, 205, 256
Horoscopic astrology, 194, 196, 204, 256
Hour circle, 191

Hsiu, Chinese lunar mansion, 182, 183, 210,
211, 224 ;

names with component stars, 210, 211 ;

starting of, 183
Huviska, 231
Hypatia, 204

Ibn Yunus, 206
Idavataara, 225
Ides, 168
Idvatsara, 225
Iliad, 201

Indian Calendar ,246
Indian Ephemeris, An, 101
Indian Ephemeris and Nautical Almanac,

5, 8, 12, 14, 17
Indra, Indian god, 199, 215, 216
Indus, river, 157
Intercalary month ( = malamasa), 175, 176,
245, 246j

Babylonian calendar, 176 ;

calculation of, 246, 249 ;

definition of 247 ;

eight-year cycle, 202 ;

Islamic calendar, 180 ;

Jewish calendar, 179 ;

list of acc. to modern calculations, 250 ;

list of according to S. S., 250 ;

19-year cycle, 176, 200, 202, 229, 245, 246 ;

Paitamaha Siddhanta, 223 ;

Rg-Veda^lMlS;.

Romaka Siddhanta, 237 ;

Siddhanta Jyotisa, 246, 248 ;

Vedanga Jyoliga, 223, 224, 225, 246

Introduction to the History of Science, 159
Isis, Egyptian god, 164, 165

Jacobi, 215

Jaikadeva, 254

Jai Singh of Amber, 10

Jamotika, 6aka king, 233

JanmaHamI, 19

Jatakas, 239

Jayanti, names of, 107

Jay as wall, 255

Jehonika, 230

Jelaluddin, Melik Shah, 166
Johann Werner, 206
Jones, Sir Harold Spencer, 6, 12, 158
Jovian cycle, 257

Jovian (Barhaspatya) years, 270 ;

names of, 270
Julian days. 161, 162
Julian days of important events, 162, 163
Julian period, 162

.Julius Caesar, 2, 10, 159, 165, 168, 241
Junction stars, of'naksatra, 184, 210, 211*. 900 ;
262-265 ;

dhruvaka of, 261, 205 ;
latitude oi (1950), 220, 264, 265 ;

(1956), 184, 210, 211 ;
long, of (1956), 230, 264. 265 ;

(1956), 184. 210. 211 ;
magnitude of, 210, 211, 264, 265
Jupiter, planet, 194, 195, 203, 239 ;

sidereal period of. 270
Jya (chord), 204
Jyoti>a Karanda, 223

Kabishak, 180

Kadamba, pole of the ecliptic, 192

Kala or liptika, 160

Krdaloka Prakasa, 223

Kalasang (inscription), 229

KalastamT, 108

Kaldarra (inscription), 229

Kalends, 168

Kalhana, Historian of Kashmir, 252
Kali, 162 ; long, of planets at Kali beginning
253

Kalidasa, 7, 261

Kalpa, 162, 175, 214, 240, 268, 269

Kalpadi, names of, 107

Kandahar, 229

Kaniska, 230, 231, 236, 256

Kanaka I, 231

Kaniska II, 232

Kaniska III, 231, 232

Kaniska Casket (inscription), 230

Kaniza Dheri (inscription), 231

Kanva, 213, 228

Kapisthala Ka^ha Samhita, 218
Kapsa, 230
Karana, 163

Karanas, definition, names and calculation of,

110 ; lords of, 110
Kanaka, 218

Kaurpa (name of a sign), 193

276

INDEX

Kautllja, views on astrology, 236
Keith, Or. Berriedale, 218
Kendra, 236. 266
Kepler, 2, 206, 242
Ketu (node), 186
Kbalatse (inscription), 229
Khav4akhadyaka of Brahmagupta, 162. 240-
253

Kharorthi (inscription), 229, 230, 231, 233
Khotani 6a ka (language), 231
Kidinnu, 200

Konow, Dr. Sten, 229, 231, 255
Kranti (declination), 262
Krttikas, 182, 219, 252
Ksaya month, 247, 248 250
Kugler, 176, 196, 225
Kumbha mela, 6
Kumbha yoga, 108
Kurram (inscription), 230
Kuruksetra, latitude of, 225
KuSanas, 213, 230-234, 236, 252, 256

Lagadha, 214, 222

Laghumanasa of Mnnjala, 162, 267

Lagna (orient ecliptic point), 237, 268

Lagrange, 167

Lalla, on precession 267

Lambaka (co-latitude), 239

Lanka. Greenwich of ancient India, 239, 253

Laplace, 167

Latitude, celestial, 192,203, 204, 210, 211, 264
265;

polar, 192, 263, 264, 265
Leap year, 6, 13, 15 ; of Islamic calendar, 180 ;

of Reformed Calendar of India, 186
Leonardo of Pisa, 160
Leeuw, Mrs. Van Lohuizen, 232, 255, 256
libra, first point of, 192, 199, 239, 262, 268
liptika, 160, 236, 263, 266
Lockyer, Sir Norman, 190
Lokambhaga of Simhasuri, 233
Longitude, celestial, 7, 192, 203, 204, 210, 211

253, 264, 265 ;

polar, 192, 263, 264, 265
Longitudes of planets at Kali-beginning, 253
Ltiders, 228, 232
Lunar eclipse, 185
Lunar mansions, 182 ;

of Rg Veda, 217 ;

stars of, 210, 211
Lunar year, beginning of, 220, 221
Lunation, duration of, 158, 174, 175, 246 ;

length of, 164, 248

Madhyahna, 101, 108

170, 183, 185,219, 221, 227, 228,

239, 252 ;

month reckoning in, 185 ;

time of compilation, 226, 252
Mahadvadasi, defined, 107
Mahftyuga, 160, 162, 217, 254
Maira (inscription), 229
Maitrayanl Sarhhita, 218
Mal&m&sa, 246, (see also intercalary month),
Mamine Pherl (inscription), 231

Miinikiala (inscription), 230
M&nsehra (inscription), 229
Manvadi, names of, 107

Manzil, Arabian lunar mansion, 182, 183,
210, 211 ;

names with component stars, 210, 211 ;

starting of, 183
Marguz (inscription), 229
Mars, planet, 194, 195, 203, 239 ;

retrograde motion of, 194
Masakrt, 174
Matins, 159
Maues, 230, 233
Mauryas, 228
Max Miiller, 183, 214, 215
Maya, 236, 238
Mean solar day, 157, 158
Mean solar time, 158
MeghadTda of Kalidasa, 261
Melik Shah the Seljuk, 159
Menander, 213, 229, 235
Menelaos (Greek astronomer), 204 ;

Spherical trigonometry, 204
Mercedonius, 168
Mercury, planet, 194, 195, 203, 239
Meridian passage, 57
Mesadi, 239

Mesadi, sidereal, 16, 17, 40
Meton of Athens, 176, 202 ;

ninetcen-year cycle, 202
Metonic cycle, 162, 176
Milimla Panho (philosophical treatise), 229
Mithra (Persian god), 167, 170
Mithradates I, 213, 255
Mithradates II, 213, 255
Mitra, Indian god, 215
Moga, £aka king, 230
Mohammed Ajmal Khan, 180
Mohammed, Prophet, 159, 179, 180
Mohenjodaro, 212
Moise of Khorene, 232
Month, anomalistic, 197 ;

beginning in Babylonian calendar, 185 ;
definition of, 157, 158, 185 ;
draconitic, 186, 197 ;
intercalary {sec intercalary month) ;
Lunar, 220, 221, 225, 245, 246 ;

commencement of as recommended

by the Committee, 7 ;
names of Indian, Chaldean and
Jewish, 177 ; Macedonian, 177, 229 ;
length of Islamic, 180 ;
interpretation of month names, 221 ;
length acc. to S. S-, 246
reckoning in Mahabharata, 185 ;
relation between draconitic and synodic,

186;
sidereal, 223 ;

Solar, causes of variation in length, 243 ;
commencement of, 7 ;
definition of, 242 ;

different conventions in beginning

of, 244;
duration of, 243 *,
Egyptian, 164 ;
first month of the year, 5, 6 ;

Month, Solar— contd,

Iranian names, 166 ;
length of, 211, 242-246, 251 ,
length recommended by the

Committee 2, 5, 6, 13, 15 ;
names in French Revolution

calendar, 167 j
names in Yajur-Veda, 218 ;
names of, Indian 5, 6, 7, 14, 15 ;
names, Persian 166, 167 ;
number of days in Vedanga Jyotisa,

225;

variation in length, 1
Synodic period, 197, 223
Moon, crescent of, 182 ; .

deviation of path from the ecliptic, 192,
208;

inclination of path to the ecliptic, 201 ;

limiting values of true motion, 197 ;

mean daily motion, 197 ;

motion of, 182 ;

movement of, 31, 181, 182 ;

rate of motion over the sun, 184 ;

sidereal period of, 182 ;

synodic period of. 182
Mount Banj (inscription), 229
Mucai (inscription), 229
Muhurta, 100, 108, 160 ; lords of, 109
Mukhya man a, 247, 249
Mtd Apin, Babylonian astrological text, 198
Munievara, commentator, 267
Munjala Bhata, 11, 259

on precession, 267-269
Mural quadrant, 203

Nabu Nazir, 177
Naburiannu, 200
Nadir, 157
Nagabha^a, 257
Nahapana, 233

Naksatra, average length of, 224 ;
beginning of, 14, 229 ;
calculation of (acc. to the recommenda-
tions of the Committee), 5, 7, 16, 17 ;
component stars of, 210, 21 1^
def. of in earliest times, 183. ,218, 227
def. of in Vedanga Jyotisa, 183, 223-225 ;
designation of, 182, 183 ;
division of, 183, 184, 219 ;
junction-stars of, 184, 210, 211, 220 r

264,265;
lords of, 109 ;

meaning of Indian, 182, 210, 211 ,
names of-general 210, 211, 263 ;
„ Tamil, 109;
„ „ -Yajur Vedic with presiding
deities, 220 ;
number of, 182 ;
Kg- Vedic, 183 ;

shifting of the beginning of, 18, 19 ;

starting of 182, 183
Nandsa Yupa inscription, 254
Napolean Bonaparti, 168
Narseh, Sassanid king, 232
Nasatya,215
Nasik,228

INDEX

277

National Observatory, 5, 8, 12, 14
Nautical Almanac, 3, 165
Nepthys, 164

Neugebauer, O., 3, 160, 175, 185, 189, 192,

198, 199, 201, 203, 204
New Testament, 169
Newton, Isaac, 2, 193, 206, 240, 259 ;

precession of the equinoxes, 207
Night, definition of, 157
Nile flood, 158, 164, 165, 174, 189
Nineteen-year cycle, 176, 200
Nirayaua, 259, 260, 262, 268
Nirt,iaya Sindhu, 101
Nirukta, 214

Nirvana, Buddha, 235, 257

Nisan, 161, 170, 175, 178, 179, 229

Nisitha, 108

Nodes, 185, 186, 187, 269

Nona, 159

Nones, 168

Numa Pompilius, 168
Nut, 164
Nutation, 209
Nychthemeron, 157, 159

Obliquity, of the ecliptic, 158, 191, 207, 208, 225
amount of, 191 ;
definition of , 191 ;
^Vctaeteris, 176
Octavious Caesar, 168 ;
Odyssey, 201
Olympiads, 178
Omar Khayyam, 166, 172, 240
Omina, 19,3, 235
Orbit, of the earth, 207
Orion, 189
Orion, 190, 195
Osiris, Egyptian god, 164

Paikuli (inscription), 232
Paitamaka Siddhanta, 223
Paja (inscription), 229
Pakaa, 227-231 ;

krsna or vahula, 15, 221, 228, 233, 247 ;

iukla, 15, 221, 228, 247 ;
Pala, 160
Palas, 257
Pallavas, 256
Pancangas,. list of, 21, 22

Panca Siddhlntifca of Varahamihira, 158, 162,

197,223,226, 236, 237, 238
Panemos, Greek month, 230
Panini,2l4

Panjtar (inscription), 229
Pannekoek, Dr. Anton, I'M, 176,178.185,194,
196, 197

Paraviddha, 101, 108 ; rules for, 109
Parivatsara, 225
Passpv^r last, 170
Pataliputra, 10, 213, 234, 252.
Paultia Siddkinta^ffli
Paulus of Alexandriav204* 23?
Perihelion, 242*, mbkfem^m.t of j.S*3
Peshawar Museum (inscription), 229. 230
Philhellens, 213

Phraates 1, 213

Pictorial Astronomy, 194, 195
PUlai, a K., 101, 223
Pingala, 214

Planet, 169 ; order of distance, 203 ;

references in Rg-Veda, 212 ;
Planetarium, 203

Planetory Astrology, 169, 194—196
Plato, 202, 203, 228, 229 ; geometry, 202
Pleiades, 182, 190, 195, 199, 219
Polar axis, 208

Polaris {< Ursae Minoris), 190, 207, 239
Pole, celestial, 191, 192, 207 ;

definition of, 191 ;

motion of, 207 ;

observation of, 190, 191 ;

precessional path of, 207
Pope, Gregory XIII, 159, 172
Pradosavrata, 108
Prahara, 160
Prajapati, 217

Prana (division of time), 160
Pratali, 108

Precession of the equinoxes, 2, 7, 8, 193, liOO,

204-206, 237, 238, 240, 253, 259, 267 ;

Al-Baftani's rate of, 206 ;

among Hindus, 226 ;

among Indian astronomers, 267 ;

amplitude of precessional oscillation
according to S. S., 268 ;

Bhaskariicarya's rate of, 269 ;

consequences of, 205, 206 ;

discovery of, 204, 205 ;

effect in Indian calendar, 7, 11, 18 ;

effect in Indian Siddhfuitas, 226 ;

explanation by Neffton, 207, 208 ;

Hipparchos's rate of, 205 ;

motion of (precessional), 208, 268 ;

Munjala Bhata's rate of, 268 ;

numerical value of, 209 ;

physical explanation of, 207, 208 ;

Prthudaka Svaml's rate of, 268 ;

Ptolemy's rate of, 205 206 ;

rate of annual, 209 ;

rate of lunar, 208, 209 ;

rate of solar, 208, 209 ;

Surya Siddhanta's rate of, 268
Prthudaka Svami, 259, 268, 269
Proclos, on precession, 206
Ptolemy, Claudius, 161, 165, 166, 177, 178, 185,

192, 200, 201, 203-206, 214, 228, 238, 24C,

263, 266 ;

on astrology, 205 ;

„ evection, 204 ;

„ rate of precession, 205 ;

„ theory of planetary motion, 204 ;
Ptolemies, 213
Ptolemy, Euergetes, 165
Pulakesin I, 233
Pulakesb -It,'35ff
Pulastya, 236
Puranas, 101, 252

Purnimfinta; moath, 157, 227,, 230, 231, 2S3,

247, 256
Puruspur, 232
Purvahna, 101, 108
PurvavidttBa^Wt,a08-p«iA» *rt?3fl9

Puskalavati, 230

Pythagorean number, 198 ;(fig.)

Quartz clock, 12, 159
Questionnaire, regarding calendar, 22 ;
replies to, 23-31

Ha, Egyptian sun-god, 164
Kahu, ascending node, 186
Ramaya^ta, 261
Kampurva (inscription), 227
Rahganatha, 233
Kapson, 255

Refraction, 225, 226 ; effect of, 225
Retrograde motion, 169, 194, 195
-ttg-Samhita, 217, 218

Biy-Vedas,V&, 212, 214, 216, 217, 218, 221,
222 ;

calendaric references in, 216-218 ;
description of, 215 ;
Ribhus, 216

Right ascension, 192, 204

Riza Shah Pahlavi ; 167

Romaka, 236,*239

Rome, Era of foundation of, 178

Rotation of the earth, 157, 158

Rudiadanian, 233

Rudra Simha,' baka satrap, 231, 236

Sachs, A., 199, 201

Saha, Prof. M. N„ 173, 232, 252, 256

Sahdaur A (inscription), 229

Sahdaur B (inscription), 229

Sahni, Dayaram, 232

6akas, 213, 230, 233, 236

Sakadvipl Brahmanas, 214, 236, 256

6a k a samvat, 2o5

fiakasthan, 213. 233

6akendra kala, 255

£alivahana &aka, 255

Samarkand, 10

Sama Veda, 214, 218

Samhitas, 214, 218

Samkranti, 2, 7, 239, 244 ;

Mahavisuva, 215 ;

Makara, 215

rules of, 244, 247, 259 ;

Uttarayana, 215 j
Sampat calana, 269
Samudragupta* 255
Samvatsara, 255, 270
Sangava, 108
6anku (gnomon), 188
6ara (celestial latitude), 262
.Sargon I, 215
Saros, 184, 185, 202,217
Sarton, George, 159, 188, 203, 204, 206
Wastry, Mm. ;Bapudev, 259
pastry, Prof. Mm. Bidhusekhar, 235
fSatakarni, 228, 233
(Satananda, 160

Satapatha Brahma^a, 18, 189, 219
^yljha^aa, 212+213, 227-231, 233, 234, 255,
Saturn, planetx,^, 195, 203^239

278

INDEX

Saura day, 197

S&vana, 2, 157, 223, 224
S&yahna, 106

Sayana, 1, 11, 12, 13, 217, 259
Bcaliger, Joseph, 9, 11, 161
Scaliger, Julius, 162
Schmidt, Dr. Olaf, 163
Schrader, 215
Scientific American, 190
Scorpion, 193, 195, 198
Scythian Period of Indian History, 232, 255
Seasons, 157, 158, 174, 189, 216, 217, 227,230, 239
causes of, 259 ;

determination by gnomon, 189
error in counting, 260 ;
length of, 174, 175, 261 ;
moving back of, 18 ;
names of Indian, 217, 241, 260 ;
position of, 1, 6, 260 ;

relation of months with seasons in Vedic
age, 216, 218 ;

in £g-Veda, 216, 217
Seb, Egyptian god 164
Seleucus, 178, 213, 228
Senas, Hindu ruling dynasty, 257
Seneca, 225

Sengupta, P. C, 183, 215, 221, 227, 238, 253,
266

Set, Egyptian god, 164
Sewell, K. S., 246
Sezta, 159

Shahpur I (Sassanid king), 232
Shama Sastry, Dr. R., 223, 224
Shin Kot (inscription), 229
Siddhanta Jyotisa, 161, 221
Siddhantas, 1, 2, 3, 163, 234, .236,237, 238,
245;

Arya,238, 242,251;

Brahma, 238, 242, 251 ;

definition of, 234 ;

Paitamaha, 236-238 ;

Paulisa, 236-238 ;

Roinaka, 236, 237, 240 ;

Surya, 236, 238-244 ;

Vasistha, 236, 237
Siddhanta Bokhara of 6rlpati, 162
Si<* V-Sada Siromatii of Bbaskaracarya, 238,

_69

Sidereal time, 158

Signs, of the zodiac, 192, 193, 194, 196, 206,

223, 224, 237, 239, 240
foksa, 214

Sircar, 1>.C.,22*. 231, 233, 234

Sirius, 104

givaratri, 108

Sky and Telescope, 177

Solar day, mean, 157, 158 ;

division of, 159 ;

Solar cycle, 162 ;
Solar time, mean, 158 ;
Solstices, 188, 189, 226 ;

determination by Vedic Hindus, 266 ;

observation in Aitareya Brahmana, 266

summer, 188, 189- 192, 226, 266 ;

winter, 13, 189, 192, 223, 224, 226, 241,
259 ;

Solstitial colure, 226

Somakara, 222
Soaigenes, 168
Sothic cycle, 165
grlpati. 11,246

Srlsena, 237 ; on precession, 267

Stone-henge, 189, 190

gudi, 247, 248

Suddha, 7, 247

Sui Vihar (inscription), 230

Sulva-Sutras, 190, 214

Sun, distance from the earth, 208 ;

entry into naksatras, 15, 40 ;

mass of, 208 ;

mean daily motion, 197 ;

semi-diameter of, 225
Sun-dial, 159
Sun-rise, 15 ;

timings of certain important places, 116
Sun-set, 15

timings of certain important places, 116 ;
Sunga, 213, 228, 235
Surya Pra/napti, 223

Surya Siddhanta, 1, 2, 158, 189, 192, 203, 214,

236-240, 242-46, 250, 251, 253, 262-264,

267, 268, 270 ;

calendar in, 239, 240 ;

description of, 238, 244 ;

error in length of year, 2, 241 ;

length of the year, 2, 240, 241 ;

star positions of, 264, 205 ;

theory of trepidation, 268
Sutras, 214. 215, 221 ;

Srauta. Urhya, Dharma, Sulva, 214
Synodic period, 158, 175, 182 ;

revolution of planets acc. to P. S., 197
Syntaxis or Almagest, 192, 201, 203, 204

Taittiriya Brahmana, 182 ;

Taittirlya Samhita, 218, 220, 221, 260

Takht-i-Bahi (inscription), 229

Tantra, 163

Tarn, 229, 255

Jaxila, 213, 228, 230, 256

Taxila copper plate (inscription), 229

Taxila silver scroll (inscription), 229

Taxila silver vase (inscription), 229

Telephos of Kapsa, 230 t

Tertia, 159

Tetrabibhs, 201, 204, 205
Thabit-ibn-Qurra, 206
Thales of Miletus, 202

prediction of solar eclipse, 202 ;
Theaitetus of Athens, 202 ;
Thcon of Alexandria, 204, 206, 240 ;

on trepidation, 206, 240
Thibaut, Dr. G., 197, 223, 225, 237
Thirteen- month calendar, 171
Thoth, Egyptian god, 164
Tigris, river, 157
Tilak, B. G., 11, 189, 215, 216
Time, natural divisions of, 157-160
Timocharis, 205
Tiridatcs, 178
Tisya, 217, 227

Tithi. 183, 218, 227, 228, 230, 234, 236, 248 ;
average duration of, 221, 222, 224, 248 ;
comparison of Siddhantic and modern, 3
defined, 3, 221 ;

definition in Aitareya Brahmana, 221 ;

„ „ Siddhantas, 221 ;

,, ,, Vedanga Jyotisa, 224, 225 ;

duration of Vedic tithi, 221 ;
error in the old method, 3, 14 ;
lords of, 109 ;
measurement of, 248 ;
names of, 222 ;
numbers of, 15, 221, 222
Tiihitatvam, 101

Trepidation, theory of, 204, 206, 207,238, 240,

259, 268, 269
Tuladi, 239
Tycho Bvahe, 206

Ullulu, 170
Ulugh Begh, 10
Umbra Extensa, 204
Umbra Versa, 204
Und (inscription), 231
Upanisads, 214, 215
Urcmometry, 205
Usavadata, Saka prince, 233
Ua-alafotlika, 101
Utkramajya, 204

Uttarfiyana. 189, 219, 224, 22G, 239, 260

Vadi, 247, 248

Vaidya, Prof. R.V., 203

I Vt i dynna tht Di hs i f lyan h 101

Vajasancyi Swihhita, 218

Vajheska, 231

Van dcr Waerdcn , 160

Varahamihira, 2, 7, 192, 193, 197, 223, 226, 236,

237, 238, 240, 252, 255, 267
Varuna, Indian god, 215, 216
Vasistha, Indian sage, 236
Vasistha Siddhanta, 236, 237, 267
Vasudcva I, 231, 232
Vasudcva II, 231, 232
Vedas, description and literature, 214 ;

age of its literature, 214, 215
Vedfingas, 214, 215

Vedanga Jyotisa, 101, 217, 224, 226, 237, 240,

241,245,246;

■description of, 221-225
Vehsadjan, 232
Ventris, 202

Venus, planet, 194, 195, 198, 203, 239 ;

heliacal rising and setting of, 6, 15
( sec also Calendar for five years).
Vernal equinox, 2, 158, 226, 239, 241, 267
Vernal point, 1, 158, 205 ;

movement of, 193, 194, 205, 267
Vespers, 159

Vidyasagar, Pandit Ishwar Chandra, 260
Vighati, 160
Vikramaditya, 254, 255
Viksepa, 192,262-265,267
Virapurusadatta, 228

INDEX

279

Visnu Candra,:237 ; on precession, 267
Visuvfin, 216, 219, 221, 266
Viguvansa, 262
Vogt, 203
Vrddha Garga, 252
Vyakarana, 214

Wardak (inscription), 230

Water-clock, 157, 159

Webster, A. G., 207, 208

Week, 169, 170, 203, 223, 234. 251, 252 ;

origin and invention of, 169, 170
Winternitz, 214, 215, 218
World Calendar Association, 10, 12, 171
Worlds' day, 172, 173

Yajnavalkya Vajasaneya, 218
Yajur Veda, 182, 183, 214, 218-222 ;

Black, 218;

6ukla, 218
Yajurveda Samhita, 218
Yajus Jyotisa, 222
Yama, division of day, 160
Yamakoti, 239
Yamardha. 108
Yaska, 214
Yavanapuri, 237
Yavanas, 213, 256

Year, 216 ; beginning of, 1, 4, 6, 13, 175 ;
beginning of in Brahmanas, 241, 245 ;
beginning of lunar. 221 ;

"in Paitamaha, 223 ;
*' in S. S., 239
" religious calendar , 251 ;
" Siddhantic, 11, 241, 245 ;
" Solar, 2, 241 ;
" " Vedanga Jyotisa, 241, 245 ;

" Vedic Aryan, 216, 218 ;
definition of, 157, 158 ;
draconitic (eclipse), 186 ;
error in beginning of, 1, 13, 15, 241 ;
error in beginning of Indian solar, 2 ;
first month of, 4, 6, 241, 242, 251 ;
Jovian (Barhaspatya), 270 ;
length (average) of Babylonian, 161, 177 ;
length of as foundby ancient astronomers,
174, 261 ;
" Brahmagupta, 162 ;
" Gregorian, 12, 13 ;
" " Paitamaha, 223, 240 ;
" " Ptolemy, 240 ;
" " sidereal, 158, 205, 240, 246 ;
" 55 solar, 223 ;

*' " Surya Siddhanta, 2,240, 241, 246'.
" " tropical, 1, 2, 4, 12, 158, 174, 175,
205, 240, 246 ;
" Varahamihira, 240 ;
*** " Vedic Aryan, 216 ;

Year— contd.

starting day of the solar, 241
Yoga, names and lords of, 110 ;

calculation of, 110
Yogatara (junction star), 183, 184, 210, 211
Yuga, 217 ;

ofEomaka Siddhanta 237

of Vedanga Jyotisa, 223, 224 ;
Yugadi, 107

Zarathustra, 167

Zeda (inscription), 230, 231

Ziggurat, 196

Zinner, Dr. Ernest, 164, 196
Zodiac, definition of, 192, 193, 202 ;
first point of , 14 ;
lunar, 182, 183, 223, 226 ;
Arabian, 182, 183 ;
Chinese, 182, 183 ;
Indian ( see naksatra)
place of origin, 183 ;
Kg Vedic, 217 ;
position through ages, 200 ;
signs of the, 193 ;
starting point of, 193 ;
zero point of the Hindu, 262, 266, 287 f
269;

Zodiacal signs, different names of, 193/see also
signs of the zodiac).

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